Deck 4: Hypothesis Tests

Question 1

The p-value is

A) the probability that the null hypothesis is true.
B) the probability that the alternative hypothesis is true.
C) the probability, when the null hypothesis is true, of obtaining a sample as extreme as (or more extreme than) the observed sample.
D) the probability, when the alternative hypothesis is true, of obtaining a sample as extreme as (or more extreme than) the observed sample.

Answer 1

the probability, when the null hypothesis is true, of obtaining a sample as extreme as (or more extreme than) the observed sample.

Question 2

A Type I error occurs by

A) rejecting the null hypothesis when the null hypothesis is false.
B) not rejecting the null hypothesis when the null hypothesis is false.
C) rejecting the null hypothesis when the null hypothesis is true.
D) not rejecting the null hypothesis when the null hypothesis is true.

Answer 2

rejecting the null hypothesis when the null hypothesis is true.

Question 3

A Type II error occurs by

A) rejecting the null hypothesis when the null hypothesis is false.
B) not rejecting the null hypothesis when the null hypothesis is false.
C) rejecting the null hypothesis when the null hypothesis is true.
D) not rejecting the null hypothesis when the null hypothesis is true.

Answer 3

not rejecting the null hypothesis when the null hypothesis is false.

Question 4

An article published in the Canadian Journal of Zoology presented a method for estimating the body fat percentage of North American porcupines; the method was illustrated with a sample of n = 25 porcupines. Based on this sample, a 95% bootstrap confidence interval for the average body fat percentage of porcupines is 17.4% to 25.8%. Which of the following null hypotheses would be rejected based on this confidence interval?

A) 18.6%
B) 26.6%
C) 20.0%
D) 22.9%

Question 5

The following figure shows a randomization distribution for the hypotheses versus . The statistic used for each sample is . Which of the two possible sample results provides the most evidence against H_o?

A)
B)

Question 6

Of the two p-values, which provides more evidence against H_o?

A) p-value = 0.41
B) p-value = 0.045

Question 7

It is of interest to test the hypotheses H_o: p = 0.8 versus H_a: p < 0.8. The sample outcome, based on n = 10 observations, is $\hat{p}$ = 0.7, and the randomization statistic to be calculated is $\hat{p}$ . The p-value for this test was found to be 0.322. If the test was performed correctly, where should the randomization distribution be centered?

A) 0.7
B) 10
C) 0.8
D) 0.322

Question 8

The average SAT-Critical Reading score for college bound students taking the exam in the 2009-2010 academic year was 501. A highly selective university wants to know if their 2010 incoming class had an average SAT-Critical Reading score that was higher than the national average. Which of the following possible samples provides the most evidence for this claim?

A) Sample A
B) Sample B
C) Sample C
D) Sample D

Question 9

Using a significance level of 5%, the appropriate conclusion for a test with a p-value of 0.0421 would be:

A) Reject H_o
B) Do not Reject H_O

Question 10

It is believed that about 37% of college students binge drink (5 or more drinks for men, and 4 or more drinks for women, in two hours). Administrators at a small university of 6,000 students want to do a study to determine if the proportion of their students who binge drink differs from 37%. They select a sample of 98 students enrolled at the university to survey about their drinking behavior. When generating the randomization distribution for this test, how large should each individual randomization sample be?

A) 98 because that is the size of the original sample
B) 1,000 to get an accurate randomization distribution
C) 6,000 because that is the size of the university
D) 2,220 because that is 37% of the students at the university

Question 11

Suppose that a 95% confidence interval for is (54.8, 60.8). Which of the following is most likely the p-value for the test of versus ? ?

A) 0.031
B) 0.001
C) 0.016
D) 0.231

Question 12

The significance level, , represents the tolerable probability of making a Type II error.

Question 13

A statistical test uses data from a sample to assess a claim about a population.

Question 14

When generating a randomization sample, the sample should be consistent with the ________________ hypothesis.

Question 15

Use the following
Match each p-value to the most appropriate conclusion.

-________ "The evidence against the null and in favor of the alternative is very strong.

A) 0.0001
B) 0.0735
C) 0.6082
D) 0.0361

Question 16

Use the following
Match each p-value to the most appropriate conclusion.

-________ "The result is significant at the 5% level but not at a 1% level."

A) 0.0002
B) 0.0736
C) 0.6083
D) 0.0362

Question 17

Use the following
Match each p-value to the most appropriate conclusion.

-________ "There is really no evidence supporting the alternative hypothesis."

A) 0.0003
B) 0.0737
C) 0.6084
D) 0.0363

Question 18

Use the following
Match each p-value to the most appropriate conclusion.

-________ "The evidence against the null is significant, but only at the 10% level."

A) 0.0004
B) 0.0738
C) 0.6085
D) 0.0364

Question 19

Identify the error in the following hypotheses: versus .

Question 20

Identify the error in the following hypotheses: versus .

Question 21

Identify the error in the following hypotheses: H_o: p = 30 versus H_a: p > 30.

Question 22

The null and alternative hypotheses for a test are H_o: p = 0.6 vs. H_a: p > 0.6. Give the notation for a sample statistic we might record for each simulated sample to create the randomization distribution.

Question 23

Use the following
Consider testing the hypotheses H_o: p = 0.4 versus H_a: p > 0.4. Four possible sample statistics, along with four possible p-values, are given. Match the statistics to their p-values.

-________ p-value = 0.72

A)
B)
C)
D)

Question 24

Use the following
Consider testing the hypotheses H_o: p = 0.4 versus H_a: p > 0.4. Four possible sample statistics, along with four possible p-values, are given. Match the statistics to their p-values.

-________ p-value = 0.293

A)
B)
C)
D)

Question 25

Use the following
Consider testing the hypotheses H_o: p = 0.4 versus H_a: p > 0.4. Four possible sample statistics, along with four possible p-values, are given. Match the statistics to their p-values.

-________ p-value = 0.138

A)
B)
C)
D)

Question 26

Use the following
Consider testing the hypotheses H_o: p = 0.4 versus H_a: p > 0.4. Four possible sample statistics, along with four possible p-values, are given. Match the statistics to their p-values.

-________ p-value = 0.019

A)
B)
C)
D)

Question 27

The randomization distribution for testing the hypotheses versus is provided. The sample statistic is . Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this test.

Question 28

The provided figure displays the randomization distribution for testing versus .

The p-value for the sample mean is closest to

A) 0.01
B) 0.25

Question 29

Briefly explain the difference between a "bootstrap distribution" and a "randomization distribution".

Question 30

Decreasing the significance level of a hypothesis test (say, from 5% to 1%) will cause the p-value of an observed test statistic to

A) increase.
B) decrease.
C) stay the same.

Question 31

Which of the following samples provides the most evidence that the amount of time spent studying for an exam and the grade on the exam are positively correlated?

A) Sample A
B) Sample B
C) Sample C
D) Sample D

Question 32

Use the following
A student in an introductory statistics course investigated if there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table.

-Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.

Question 33

Use the following
A student in an introductory statistics course investigated if there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table.

-Use the provided randomization distribution (based on 100 samples) to test if this sample provides evidence that the proportion of candies that are green differs for the two types of M&M's. Include an assessment of the strength of your evidence.

Question 34

Use the following
A student in an introductory statistics course investigated if there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table.

-Use technology and the provided data to test if this sample provides evidence that the proportion of candies that are green differs for the two types of M&M's. Include an assessment of the strength of your evidence.

Question 35

Use the following
A student in an introductory statistics course investigated if there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table.

-Define the appropriate parameter(s) and state the hypotheses for testing if the proportion of green M&M's differs for milk chocolate and dark chocolate M&M's.

Question 36

Use the following
A student in an introductory statistics course investigated if there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table.

-Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.

Question 37

Use the following
A student in an introductory statistics course investigated if there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table.

-Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses. Use your randomization distribution to estimate the p-value for this sample.

Question 38

Use the following
A student in an introductory statistics course investigated if there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table.

-Use your p-value to make a decision about these hypotheses. Be sure to word your decision in the context of the problem. Include an assessment of the strength of your evidence.

Question 39

Use the following
A student in an introductory statistics course investigated if there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table.

-Define the appropriate parameter(s) and state the hypotheses for testing if the proportion of green M&M's differs for milk chocolate and dark chocolate M&M's.

Question 40

Use the following
A student in an introductory statistics course investigated if there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table.

-Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.

Question 41

Use the following
A student in an introductory statistics course investigated if there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table.

-Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample.
‪

Question 42

Use the following
A student in an introductory statistics course investigated if there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table.

-Use your p-value to make a decision about these hypotheses. Be sure to word your decision in the context of the problem. Include an assessment of the strength of your evidence.

Question 43

Use the following
As of August 8, 2012, the national average price for a gallon of regular unleaded gasoline was $3.63. The prices for a sample of n = 10 gas stations in the state of Illinois are provided.

It is of interest to use this sample to compare the average gas price in Illinois to the national average.
-Describe how you could generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.

Question 44

Use the following
As of August 8, 2012, the national average price for a gallon of regular unleaded gasoline was $3.63. The prices for a sample of n = 10 gas stations in the state of Illinois are provided.

It is of interest to use this sample to compare the average gas price in Illinois to the national average.
-Use the provided randomization distribution (based on 1,000 samples) to test if this sample provides evidence that the average gas price in Illinois exceeds the national average. Include an assessment of the strength of your evidence.

Question 45

Use the following
As of August 8, 2012, the national average price for a gallon of regular unleaded gasoline was $3.63. The prices for a sample of n = 10 gas stations in the state of Illinois are provided.

It is of interest to use this sample to compare the average gas price in Illinois to the national average.
-Use technology and the provided data to test if this sample provides evidence that the average gas price in Illinois exceeds the national average. Include an assessment of the strength of your evidence.

Question 46

Use the following
As of August 8, 2012, the national average price for a gallon of regular unleaded gasoline was $3.63. The prices for a sample of n = 10 gas stations in the state of Illinois are provided.

It is of interest to use this sample to compare the average gas price in Illinois to the national average.
-Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that the average gas price in Illinois exceeds the national average.

Question 47

Use the following
As of August 8, 2012, the national average price for a gallon of regular unleaded gasoline was $3.63. The prices for a sample of n = 10 gas stations in the state of Illinois are provided.

It is of interest to use this sample to compare the average gas price in Illinois to the national average.
-Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.

Question 48

Use the following
As of August 8, 2012, the national average price for a gallon of regular unleaded gasoline was $3.63. The prices for a sample of n = 10 gas stations in the state of Illinois are provided.

It is of interest to use this sample to compare the average gas price in Illinois to the national average.
-Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses. Use your randomization distribution to estimate the p-value for this sample.
‪

Question 49

Use the following
As of August 8, 2012, the national average price for a gallon of regular unleaded gasoline was $3.63. The prices for a sample of n = 10 gas stations in the state of Illinois are provided.

It is of interest to use this sample to compare the average gas price in Illinois to the national average.
-Use your p-value to make a decision about these hypotheses. Be sure to word your decision in the context of the problem. Include an assessment of the strength of your evidence.

Question 50

Use the following
As of August 8, 2012, the national average price for a gallon of regular unleaded gasoline was $3.63. The prices for a sample of n = 10 gas stations in the state of Illinois are provided.
It is of interest to use this sample to compare the average gas price in Illinois to the national average.
-Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that the average gas price in Illinois exceeds the national average.

Question 51

Use the following
As of August 8, 2012, the national average price for a gallon of regular unleaded gasoline was $3.63. The prices for a sample of n = 10 gas stations in the state of Illinois are provided.
It is of interest to use this sample to compare the average gas price in Illinois to the national average.
-Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.

Question 52

Use the following
As of August 8, 2012, the national average price for a gallon of regular unleaded gasoline was $3.63. The prices for a sample of n = 10 gas stations in the state of Illinois are provided.
It is of interest to use this sample to compare the average gas price in Illinois to the national average.
-Use the provided randomization distribution (based on 1,000 samples) to estimate the p-value for this sample.

Question 53

Use the following
As of August 8, 2012, the national average price for a gallon of regular unleaded gasoline was $3.63. The prices for a sample of n = 10 gas stations in the state of Illinois are provided.
It is of interest to use this sample to compare the average gas price in Illinois to the national average.
-Use your p-value to make a decision about these hypotheses. Be sure to word your decision in the context of the problem. Include an assessment of the strength of your evidence.

Question 54

Use the following
A study recently described in Attention, Perception, and Psychophysics investigated the impacts of mult-tasking on people who play video games and those who don't. Participants in the study were asked to perform three visually demanding tasks with (dual-task) and without (single-task) answering unrelated questions over the phone. One of the tasks involved tracking multiple circles moving around on a computer monitor. At the 5% significance level, the authors of the study concluded "tracking accuracy was significantly worse in the dual-task condition"
for both people who play video games and those who do not.

-What conclusion would the authors have made at the 10% significance level?

A) Tracking accuracy was significantly worse in the dual-task condition.
B) Tracking accuracy was not significantly worse in the dual-task condition.
C) Not enough information

Question 55

Use the following
A study recently described in Attention, Perception, and Psychophysics investigated the impacts of mult-tasking on people who play video games and those who don't. Participants in the study were asked to perform three visually demanding tasks with (dual-task) and without (single-task) answering unrelated questions over the phone. One of the tasks involved tracking multiple circles moving around on a computer monitor. At the 5% significance level, the authors of the study concluded "tracking accuracy was significantly worse in the dual-task condition"
for both people who play video games and those who do not.

-What conclusion would the authors have made at the 1% significance level?

A) Tracking accuracy was significantly worse in the dual-task condition.
B) Tracking accuracy was not significantly worse in the dual-task condition.
C) Not enough information

Question 56

Use the following
A study recently described in Attention, Perception, and Psychophysics investigated the impacts of mult-tasking on people who play video games and those who don't. Participants in the study were asked to perform three visually demanding tasks with (dual-task) and without (single-task) answering unrelated questions over the phone. One of the tasks involved tracking multiple circles moving around on a computer monitor. At the 5% significance level, the authors of the study concluded "tracking accuracy was significantly worse in the dual-task condition"
for both people who play video games and those who do not.
-What does the phrase "significantly worse" mean in this context?

Question 57

Use the following
A study recently described in Attention, Perception, and Psychophysics investigated the impacts of mult-tasking on people who play video games and those who don't. Participants in the study were asked to perform three visually demanding tasks with (dual-task) and without (single-task) answering unrelated questions over the phone. One of the tasks involved tracking multiple circles moving around on a computer monitor. At the 5% significance level, the authors of the study concluded "tracking accuracy was significantly worse in the dual-task condition"
for both people who play video games and those who do not.
-Which type of error, Type I or Type II, could have occurred in this situation? Briefly justify your answer.

Question 58

Use the following
In 2012 the Centers for Disease Control and Prevention reported that in a sample of 4,349 African Americans 31% were Vitamin D deficient. A 90% confidence interval based on this sample is (0.30, 0.32). It is believed that among the general population of Americans 8% suffer from Vitamin D deficiency.
-Define the appropriate parameter and state the appropriate hypotheses for testing the claim that, among African Americans, Vitamin D deficiency occurs at a rate other than 8%.

Question 59

Use the following
In 2012 the Centers for Disease Control and Prevention reported that in a sample of 4,349 African Americans 31% were Vitamin D deficient. A 90% confidence interval based on this sample is (0.30, 0.32). It is believed that among the general population of Americans 8% suffer from Vitamin D deficiency.
-Does this confidence interval provide evidence that among African Americans Vitamin D deficiency occurs at a rate other than 8%? What significance level is being used to make this decision? Briefly justify your answer.

Question 60

The provided histogram displays the prices (in thousands of dollars) of 17 homes sold between November 2011 and February 2012 in a Midwestern city.

In general this shape, right skewed with some unusually high values, is common for describing home values in many cities. For this reason, the median home value for a city is a useful parameter. This sample of recently sold homes had a median price (value) of $166,500. Someone considering moving to this city is interested in knowing if the median home value is more than $150,000.
Describe how you would generate a single randomization sample in this situation, and identify the statistic you would calculate from the sample.

Question 61

Using the definition of a p-value, explain why the area in the tail of a randomization distribution is used to compute a p-value.

Question 62

In a test of the hypotheses versus , the observed sample results in a p-value of 0.0256. Would you expect a 95% confidence interval for based on this sample to contain 0? Briefly explain why or why not.

Question 63

In August 2012 Gallup reported the results from a survey of 177,663 U.S. adults from January - June 2012 for the Gallup-Healthways Well-Being Index. Based on self-reported height and weight data, they found that 62.8% of U.S. adults are overweight or obese. A 95% confidence interval for the proportion of U.S. adults that are overweight or obese is (0.626, 0.63). Does this interval support the claim that "two-thirds of Americans are overweight or obese"? Briefly justify your answer.

Question 64

Use the following
The makers of a popular brand of laundry detergent have discovered a new secret ingredient that they believe will boost the cleaning power of their detergent. The new ingredient is expensive, and if they use it, they would have to increase the retail price of the detergent (and they worry that the price increase will cause them to lose customers). However, they believe that if the improved detergent gets clothes drastically cleaner, customers will recognize that it is worth the extra cost. They conduct an experiment to compare the performance of the new and old formulas at removing grass stains, red wine, and chocolate from white t-shirts. Each cleaned shirt was rated on a scale from 1 (stain did not get removed) to 10 (no evidence of the stain) by trained experts. They compared the average rating for the new and old formulas.
-Briefly explain what a Type II error would mean in this situation.

Question 65

Use the following
The makers of a popular brand of laundry detergent have discovered a new secret ingredient that they believe will boost the cleaning power of their detergent. The new ingredient is expensive, and if they use it, they would have to increase the retail price of the detergent (and they worry that the price increase will cause them to lose customers). However, they believe that if the improved detergent gets clothes drastically cleaner, customers will recognize that it is worth the extra cost. They conduct an experiment to compare the performance of the new and old formulas at removing grass stains, red wine, and chocolate from white t-shirts. Each cleaned shirt was rated on a scale from 1 (stain did not get removed) to 10 (no evidence of the stain) by trained experts. They compared the average rating for the new and old formulas.
-Suppose they find that the average rating for the shirts cleaned with the new formula was 8.2 and the average rating for the shirts cleaned with the old formula is 8.0 (p-value = 0.046). Do you think these results are practically significant? Briefly explain.

Question 66

Use the following
The makers of a popular brand of laundry detergent have discovered a new secret ingredient that they believe will boost the cleaning power of their detergent. The new ingredient is expensive, and if they use it, they would have to increase the retail price of the detergent (and they worry that the price increase will cause them to lose customers). However, they believe that if the improved detergent gets clothes drastically cleaner, customers will recognize that it is worth the extra cost. They conduct an experiment to compare the performance of the new and old formulas at removing grass stains, red wine, and chocolate from white t-shirts. Each cleaned shirt was rated on a scale from 1 (stain did not get removed) to 10 (no evidence of the stain) by trained experts. They compared the average rating for the new and old formulas.
-Suppose, at the 5% significance level, they find that the new formula cleaned the shirts significantly better than the old formula, with a p-value of 0.046. Interpret the p-value, in terms of the probability of the results happening by random chance, in this context.

Question 67

Use the following
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. The average age of the trees in the sample is about 120 years. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.
-Describe how you would generate a single randomization sample in this situation, and identify the statistic you would calculate for each sample.

Question 68

Use the following
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. The average age of the trees in the sample is about 120 years. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.
-Use the provided randomization distribution (based on 100 samples) to determine if this sample provides evidence that the average age of the driftwood along this beach is less than 130 years. Use a 5% significance level to make your conclusion.

Question 69

Use the following
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. Her data are displayed in the provided table. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.

-Describe how you would generate a single randomization sample in this situation, and identify the statistic you would calculate for each sample.

Question 70

Use the following
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. Her data are displayed in the provided table. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.

-Use technology and the provided data to determine if this sample provides evidence that the average age of the driftwood along this beach is less than 130 years. Use a 5% significance level to make your conclusion.

Question 71

Use the following
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. The average age of the trees in the sample is approximately 120 years. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.
-Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that the average age of the driftwood along this beach is less than 130 years.

Question 72

Use the following
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. The average age of the trees in the sample is approximately 120 years. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.
-Describe how you would generate a single randomization sample in this situation, and identify the statistic you would calculate for each sample.

Question 73

Use the following
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. The average age of the trees in the sample is approximately 120 years. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.
-Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample.
‪

Question 74

Use the following
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. The average age of the trees in the sample is approximately 120 years. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.
-Use your p-value and a 5% significance level to make a decision about these hypotheses. Be sure to word your decision in the context of the problem.

Question 75

Use the following
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. The average age of the trees in the sample is approximately 120 years. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.
-What conclusion would you make at the 10% significance level?

Question 76

Use the following
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. Her data are displayed in the provided table. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.

-Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that the average age of the driftwood along this beach is less than 130 years.

Question 77

Use the following
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. Her data are displayed in the provided table. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.

-Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.

Question 78

Use the following
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. Her data are displayed in the provided table. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.

-Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses. Use your randomization distribution to estimate the p-value for this sample.

Question 79

Use the following
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. Her data are displayed in the provided table. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.

-Use your p-value and a 5% significance level to make a decision about these hypotheses. Be sure to word your decision in the context of the problem.

Question 80

Use the following
A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. Her data are displayed in the provided table. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging.

-What conclusion would you make at the 10% significance level?