Deck 8: Hypothesis Testing

Question 1

The ____ is the probability of getting a test statistic at least as extreme as the one representing the sample data, assuming that the null hypothesis is true.

A) P -value
B) sample proportion
C) critical value
D) level of significance

Answer 1

P -value

Question 2

Express the original claim in symbolic form.
Claim: 20% of adults smoke

A)
B) p=0.2
C)
D)

Answer 2

p=0.2

Question 3

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol for the indicated parameter. An entomologist writes an article in a scientific journal which claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p , the true proportion of fireflies unable to produce light.

A)
B)
C)
D)

Answer 3

Question 4

A Type I error is the mistake of ________________ when it is actually true

A) failing to reject the null hypothesis
B) failing to reject the alternative hypothesis
C) rejecting the null hypothesis
D) rejecting the alternative hypothesis

Question 5

Which of the following is not a requirement for testing a claim about a population proportion?

A) The sample observations are a simple random sample.
B) The conditions for a binomial distribution are satisfied.
C) The conditions are both satisfied.
D) All of the other statements are requirements for testing a claim about a population proportion.

Question 6

Find the P-value in a test of the claim that the mean IQ score of acupuncturists is equal to 100 , given that the test statistic is z=-2.00

A)0.0228
B)0.955
C)0.977
D)0.0455

Question 7

A hypothesis test is performed to test the claim that a population proportion is greater than 0.7 . Find the probability of a type II error given that the true value of the population proportion is 0.72 . The sample size is 50 and the significance level is 0.05 .

A) 0.4129
B) 0.5754
C) 0.7123
D) 0.9706

Question 8

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of the seventh-graders at a neighboring school, which have variation described by
Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

A) There is sufficient evidence to support the claim that the standard deviation is greater than 14.7 .
B) There is sufficient evidence to support the claim that the standard deviation is less than 14.7.
C) There is not sufficient evidence to support the claim that the standard deviation is greater than 14.7.
D) There is not sufficient evidence to support the claim that the standard deviation is less than 14.7.

Question 9

Use the given information to find the P -value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). The test statistic in a right-tailed test is z=0.52 .

A) 0.6030 ; fail to reject the null hypothesis
B) 0.3015 ; reject the null hypothesis
C) 0.0195 ; reject the null hypothesis
D) 0.3015 ; fail to reject the null hypothesis

Question 10

A formal hypothesis test is to be conducted using the claim that the mean body temperature is equal to
What is the null hypothesis and how is it denoted?

A)
B)
C)
D)

Question 11

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. Carter Motor Company claims that its new sedan, the Libra, will average better than 32 miles per gallon in the city. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

A) There is sufficient evidence to support the claim that the mean is greater than 32 miles per gallon.
B) There is not sufficient evidence to support the claim that the mean is greater than 32 miles per gallon.
C) There is not sufficient evidence to support the claim that the mean is less than 32 miles per gallon.
D) There is sufficient evidence to support the claim that the mean is less than 32 miles per gallon.

Question 12

Find the critical value or values of based on the given information.

n=23

A) 14.848
B) 30.813
C) -30.813
D) 14.042

Question 13

Find the critical value or values of based on the given information.

n=19

A) 8.231
B) 31.526
C) 7.015
D) 8.907

Question 14

A chi-square hypothesis test is going to be conducted about a population standard deviation. Select the statement that is not true about the Chi-square test

A) The sample must be a simple random sample.
B) The population does not have to be a normally distributed population.
C) The alternative hypothesis must contain <,> or
D) The sample size must be known.

Question 15

Solve the problem. For large numbers of degrees of freedom, the critical values can be approximated as follows: where k is the number of degrees of freedom and z is the critical value. To find the lower critical value, the negative z-value is used, to find the upper critical value, the positive z-value is used. Use this approximation to estimate the critical value of in a two-tailed hypothesis test with n=104 and

A) X²=85.903 and X²=122.735
B) X²=81.186 and X²=128.520
C) X²=80.300 and X²=127.406
D) X²=84.992 and X²=121.646

Question 16

Suppose we want to test the claim that the majority of adults are in favor of raising the voting age to 21. Is the hypothesis test left-tailed, right-tailed, or two-tailed?

A) Left-tailed
B) Right-tailed
C) Two-tailed

Question 17

Find the value of the test statistic using
The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25 , and the sample statistics include n=696 drowning deaths of children with 30 % of them attributable to beaches.

A) 3.05
B) -3.05
C) -2.88
D) 2.88

Question 18

Use the given information to find the P -value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). With : p>0.554 , the test statistic is z=1.34 .

A) 0.9099 ; fail to reject the null hypothesis
B) 0.0901 ; reject the null hypothesis
C) 0.0901 ; fail to reject the null hypothesis
D) 0.1802 ; reject the null hypothesis

Question 19

Express the null hypothesis and the altemative hypothesis in symbolic form. Use the correct symbol for the indicated parameter. A psychologist claims that more than 5.8 percent of the population suffers from professional problems due to extreme shyness. Use p, the true percentage of the population that suffers from extreme shyness.

A)
B)
C)
D)

Question 20

Use the given information to find the P -value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). With the test statistic is =0.78 .

A) 0.2177 ; reject the null hypothesis
B) 0.4354 ; reject the null hypothesis
C) 0.4354 ; fail to reject the null hypothesis
D) 0.2177 fail to reject the null hypothesis

Question 21

Solve the problem. For large numbers of degrees of freedom, the critical values can be approximated as follows: where k is the number of degrees of freedom and z is the critical value. To find the lower critical value, the negative z-value is used, to find the upper critical value, the positive z-value is used. Use this approximation to estimate the critical value of in a right-tailed hypothesis test with n=143 and

A)
B)
C)
D)

Question 22

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. Carter Motor Company claims that its new sedan, the Libra, will average better than 32 miles per gallon in the city. Assuming that a hypothesis test of the claim has been conducted and
That the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

A) There is not sufficient evidence to support the claim that the mean is greater than 32
Miles per gallon.
B) There is not sufficient evidence to support the claim that the mean is less than 32 miles
Per gallon.
C) There is sufficient evidence to support the claim that the mean is less than 32 miles per
Gallon.
D) There is sufficient evidence to support the claim that the mean is greater than 32 miles
Per gallon.

Question 23

Solve the problem. A hypothesis test is performed to test the claim that a population proportion is greater than 0.7 . Find the probability of a type II error, , given that the true value of the population proportion is 0.72 . The sample size is 50 and the significance level is 0.05 .

A) 0.4129
B) 0.7123
C) 0.5754
D) 0.9706

Question 24

Find the P -value for the indicated hypothesis test. An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of 225 fathers from Littleton, yielded 97 who did not help with child care. Find the P -value for a test of the researcher's claim.

A) 0.0015
B) 0.0038
C) 0.0529
D) 0.0019

Question 25

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. The owner of a football team claims that the average attendance at games is over 523, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a
Hypothesis test of the claim has been conducted and that the conclusion is failure to reject the
Null hypothesis, state the conclusion in nontechnical terms.

A) There is sufficient evidence to support the claim that the mean attendance is less than
523)
B) There is not sufficient evidence to support the claim that the mean attendance is less
Than 523.
C) There is sufficient evidence to support the claim that the mean attendance is greater
Than 523.
D) There is not sufficient evidence to support the claim that the mean attendance is greater
Than 523.

Question 26

Find the P -value in a test of the claim that the mean College Algebra final exam score of engineering majors equal to 88 , given that the test statistic is z=1.50 .

A) 0.0668
B) 0.9331
C) 0.1336
D) 0.1500

Question 27

The p-value is the probability of getting a test statistic at least as extreme as the one representing the sample data, assuming that ______________________________.

A) the null hypothesis is true
B) the null hypothesis is false
C) the alternative hypothesis is true
D) the alternative hypothesis is false

Question 28

Find the critical value or values of based on the given information.
n=19

A) 8.907
B) 8.231
C) 7.015
D) 31.526

Question 29

Find the value of the test statistic z using https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/. The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25 , and the sample statistics include n=696 drowning deaths of children with 30% of them attributable to beaches.

A) 2.88
B) 3.05
C) -3.05
D) -2.88

Question 30

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol for the indicated parameter. An entomologist writes an article in a scientific journal which claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light.

A)
B)
C)
D)

Question 31

A formal hypothesis test is to be conducted using the claim that the mean AC thermostat setting in restaurants is equal to What is the null hypothesis and how is it denoted?

A)
B)
C)
D)

Question 32

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol for the indicated parameter. The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature,, of ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect.

A)
B)
C)
D)

Question 33

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. A consumer advocacy group claims that the mean mileage for the Carter Motor Company's new sedan is less than 32 miles per gallon. Identify the type I error for the test.

A) Reject the claim that the mean is equal to 32 miles per gallon when it is actually less than 32 miles per gallon.
B) Fail to reject the claim that the mean is equal to 32 miles per gallon when it is actually less than 32 miles per gallon.
C) Fail to reject the claim that the mean is equal to 32 miles per gallon when it is actually greater than 32 miles per gallon.
D) Reject the claim that the mean is equal to 32 miles per gallon when it is actually 32 miles per gallon.

Question 34

Use the given information to find the P -value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). With the test statistic is z=3.06 .

A) 0.0011 ; reject the null hypothesis
B) 0.0022 ; fail to reject the null hypothesis
C) 0.0022 ; reject the null hypothesis
D) 0.0011 ; fail to reject the null hypothesis

Question 35

A _____________ error is the mistake of rejecting the null hypothesis when it is actually true

A) Type I
B) Type II
C) Type III
D) Type IV

Question 36

Solve the problem. For large numbers of degrees of freedom, the critical values can be approximated as follows: where k is the number of degrees of freedom and z is the critical value. To find the lower critical value, the negative z-value is used, to find the upper critical value, the positive z-value is used. Use this approximation to estimate the critical value of in a two-tailed hypothesis test with n=104 and

A)
B)
C)
D)

Question 37

Which of the following is a requirement for testing a claim about a population proportion?

A) The sample observations are a stratified sample.
B) The trials are dependent.
C) The conditions and are both satisfied.
D) None of the other statements are requirements for testing a claim about a population proportion.

Question 38

Find the value of the test statistic z using
A claim is made that the proportion of children who play sports is less than 0.5 , and the sample statistics include n=1320 subjects with 30 % saying that they play a sport.

A) 14.53
B) 29.66
C) -29.66
D) -14.53

Question 39

Express the original claim in symbolic form.
Claim: 60% of homes have smoke detectors.

A)
B) p=0.6
C)
D)

Question 40

Suppose we want to test the claim that less than of Americans are in favor of raising the voting age to 21 . Is the hypothesis test left-tailed, right-tailed, or two-tailed?

A) Left-tailed
B) Right-tailed
C) Two-tailed

Question 41

Question 42

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. A manufacturer uses a new
production method to produce steel rods. A random sample of 17 steel rods resulted in lengths
with a standard deviation of 4.7 cm. At the 0.10 significance level, test the claim that the new
production method has lengths with a standard deviation different from 3.5 cm, which was the
standard deviation for the old method.

Question 43

An oil change shop claims that they will change your oil in under 15 minutes. To test this claim, a consumer advocacy group takes a simple random sample of 10 customers and records the number of minutes it took to complete oil changes for these customers. Assume that oil change times are normally distributed.

Conduct a hypothesis test for the oil shop's claim about oil change times at the 5% level of significance.

Question 44

What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the rare event rule and make a subjective estimate to determine whether
the event is likely.
Claim: A die is fair and in 100 rolls there are 63 sixes.

Question 45

Sam wanted to test a claim about the mean of a population whose standard deviation was unknown. He picked a simple random sample of size 20 from the population. Lou wanted to
test a claim about a mean of a different population whose standard deviation was known. He
picked a simple random sample of size 22 from that population. George said that Sam would
need to determine whether his sample was from a normally distributed population because the
population standard deviation was unknown. He said that Lou would not need to do this since
for his test the population standard deviation was known. Is George right?
116

Question 46

A watch manufacturer believes that 60% of men over age 50 wear watches. So, the manufacturer took a simple random sample of 275 men over age 50 and 170 of those men wore watches. Test the watch manufacturer's claim at

Question 47

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated.
Identify the null and alternative hypotheses, test statistic, critical value(s)or P-value (or range
of P-values)as appropriate, and state the final conclusion that addresses the original claim. A
public bus company official claims that the mean waiting time for bus number 14 during peak
hours is less than 10 minutes. Karen took bus number 14 during peak hours on 18 different
occasions. Her mean waiting time was 7.6 minutes with a standard deviation of 2.3 minutes.
At the 0.01 significance level, test the claim that the mean waiting time is less than 10
minutes. Use the P-value method of testing hypotheses.

Question 48

Identify the null hypothesis, alternative hypothesis, test statistic, P -value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of 234 fathers from Littleton yielded 96 who did not help with child care. Test the researcher's claim at the 0.05 significance level.

Question 49

Solve the problem. What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the rare event rule and make a subjective estimate to
determine whether the event is likely.
Claim: A roulette wheel is fair and in 40 consecutive spins of the wheel, black shows up 23
times. (A roulette wheel has 38 equally likely slots of which 18 are black).

Question 50

Solve the problem. Suppose that you are conducting a study on the effectiveness of a new teaching method and that you wish to use a hypothesis test to support your claim regarding
the mean test score under this method. What restrictions are there in the wording of the claim?
Will your claim become the null hypothesis or the alternative hypothesis, or does it depend on
the situation? Give an example of a claim which is incorrectly worded.

Question 51

Provide an appropriate response. Tim believes that a coin is coming up tails less than 50% of the time. He tests the claim p<0.5 . In 100 tosses, the coin comes up tails 57 times. What is the value of the sample proportion? Do you think the P -value will be small or large and what should Tim conclude about the claim p<0.5?

Question 52

Test the given claim. Use the P -value method or the traditional method as indicated. Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s) or P -value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. The mean resting pulse rate for men is 72 beats per minute. A simple random sample of men who regularly work out at Mitch's Gym is obtained and their resting pulse rates (in beats per minute) are listed below. Use a 0.05 significance level to test the claim that these sample pulse rates come from a population with a mean less than 72 beats per minute. Assume that the standard deviation of the resting pulse rates of all men who work out at Mitch's Gym is known to be 6.6 beats per minute. Use the traditional method of testing hypotheses.

Question 53

Identify the null hypothesis, alternative hypothesis, test statistic, P -value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of 183.9 lb . Assuming that is known to be 121.2 lb, use a 0.10 significance level to test the claim that the population mean of all such employees weights is less than 200 lb.

Question 54

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated.
Identify the null and alternative hypotheses, test statistic, critical value(s)or P-value (or range
of P-values)as appropriate, and state the final conclusion that addresses the original claim.
A cereal company claims that the mean weight of the cereal in its packets is 14 oz. The
weights (in ounces)of the cereal in a random sample of 8 of its cereal packets are listed below. Test the claim at the 0.01 significance level.

Question 55

Provide an appropriate response. Complete the following table on hypothesis testing.

Question 56

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P -values) as appropriate, and state the final conclusion that addresses the original claim. A light-bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A random sample of 15 of its light bulbs resulted in the following lives in hours.

At the 10 % significance level, test the claim that the sample is from a population with a mean life of 900 hours. Use the P-value method of testing hypotheses.

Question 57

A simple random sample of the running time of movies of 70 international movies resulted in a sample mean length of 112 minutes and a sample standard deviation of 7 minutes. Test the
claim that international movies have a mean running time of more than 110 minutes at the 5%
level of significance. Assume that the lengths of movies are normally distributed.

Question 58

Solve the problem. Use the P-value method to test the claim that the population standard deviation of the systolic blood pressures of adults aged 40-50 is equal to 22 mm Hg. The sample statistics are as follows: n=23, x=132.2 mm Hg, s=26.6 mm Hg. Be sure to state the hypotheses, the value of this test statistic, the P -value, and your conclusion. Use a significance level of 0.05 .

Question 59

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. For randomly selected adults, IQ scores are nomally distributed with a standard deviation of 15. The scores of 14 randomly selected college students are listed below. Use a 0.10 significance level to test the claim that the standard deviation of IQ scores of college students is less than 15 . Round the sample standard deviation to three decimal places.

Question 60

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. Heights of men aged 25 to 34 have a standard deviation of 2.9 . Use a 0.05 significance level to test the claim that the heights of women aged 25 to 34 have a different standard deviation. The heights (in inches) of 16 randomly selected women aged 25 to 34 are listed below. Round the sample standard deviation to five decimal places.