Deck 16: More About Tests and Intervals

Question 1

A large software development firm recently relocated its facilities.Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities.They believe that the firm's professionals volunteer an average of more than 15 hours per month.If this is not the case, they will institute an incentive program to increase community involvement.A random sample of 24 professionals yields a mean of 16.6 hours and a standard deviation of 2.22 hours.The correct value of the test statistic for the appropriate hypothesis test is

A) $t = - 3.532$
B) $t = 3.532$
C) $t = 0.789$
D) $t = - 1.223$
E) $t = 1.223$

Answer 1

$t = 0.789$

Question 2

Answer 2

B

Question 3

A company that sells eco-friendly cleaning products is concerned that only 19.5% of people who use such products select their brand .A marketing director suggests that the company invest in new advertising and labeling to strengthen its green imagE.The company decides to do so in a test market so that the effectiveness of the marketing campaign may be evaluated.
In this context, committing a Type I error
I.Occurs when they conclude that the percentage of customers purchasing the company's
Brand has increased when in fact it has not.
II.Occurs then they conclude that the percentage of customers purchasing the company's
Brand has not increased when in fact it has.
III.Would result in the company wasting money on a new marketing campaign that does not
Increase the percentage of customers buying their brand.

A)I only
B)II only
C)III only
D)Both I and III
E)Both II and III

Answer 3

Both I and III

Question 4

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 5%.Identify the Type II error in this context.

A)The error of rejecting the claim that the true proportion is at least 5% when it really is at least 5%.
B)The error of failing to reject the claim that the true proportion is at least 5% when it is actually less than 5%.
C)The error of accepting the claim that the true proportion is at least 5% when it really is at least 5%.
D)The error of rejecting the claim that the true proportion is less than 5% when it really is less than 5%.
E)The error of accepting the claim that the true proportion is at least 5% when it is actually less than 5%.

Question 5

An entomologist writes an article in a scientific journal which claims that fewer than 6% of male fireflies are unable to produce light due to a genetic mutation.Identify the Type I error in this context.

A)The error of failing to reject the claim that the true proportion is at least 6% when it is actually less than 6%.
B)The error of rejecting the claim that the true proportion is less than 6% when it really is less than 6%.
C)The error of accepting the claim that the true proportion is at least 6% when it really is at least 6%.
D)The error of failing to accept the claim that the true proportion is at least 6% when it is actually less than 6%.
E)The error of rejecting the claim that the true proportion is at least 6% when it really is at least 6%.

Question 6

Question 7

In 1990, the average math SAT score for students at one school was 472.Five years later, a teacher wants to perform a hypothesis test to determine whether the average math SAT score of students at the school has changed from the 1990 mean of 472.The hypotheses are:
H₀ :?=472
H_A : ?=472
Explain the result of a Type I error.

A)The teacher will conclude that the mean math SAT score at the school is the same when in fact it is different.
B)The teacher will conclude that the mean math SAT score at the school is the same when in fact it is the same.
C)The teacher will conclude that the mean math SAT score at the school has decreased when in fact it is the same.
D)The teacher will conclude that the mean math SAT score at the school is different when in fact it is the same.

Question 8

Top management of a large multinational corporation wants to create a culture of innovativeness and changE.A consultant hired to assess the company's organizational culture finds that only 15% of employees are open to new ideas and approaches toward their work.Consequently the company conducts a program for employees in order to reinforce the new corporate philosophy.After the program is completed, employees are surveyed to
See if a greater percentage is now open to innovativeness and changE.Suppose that based on the sample results the company rejects the null hypothesis when in fact it is truE.Which of the following statements is correct?

A)This led to the conclusion that the percentage of employees open to new ideas did not increase when in fact it did.
B)This led to the conclusion that the percentage of employees open to new ideas did increase when in fact it did not.
C)This is known as a fatal error.
D)This is known as a Type II error.

Question 9

A man is on trial accused of murder in the first degree.The prosecutor presents evidence that he hopes will convince the jury to reject the hypothesis that the man is innocent.This situation can be modeled as a hypothesis test with the following hypotheses:
$H _ { 0 }$ : The defendant is not guilty.
$H _ { A }$ : The defendant is guilty.
Explain the result of a Type II error.

A)The jury will fail to reach a decision.
B)The jury will conclude that the defendant is guilty when in fact he is not guilty.
C)The jury will conclude that the defendant is not guilty when in fact he is not guilty.
D)The jury will conclude that the defendant is guilty when in fact he is guilty.
E) The jury will conclude that the defendant is not guilty when in fact he is guilty.

Question 10

Top management of a large multinational corporation wants to create a culture of innovativeness and changE.A consultant hired to assess the company's organizational culture finds that only 15% of employees are open to new ideas and approaches toward their work.Consequently the company conducts a program for employees in order to reinforce the new corporate philosophy.After the program is completed, employees are surveyed to see if a greater percentage is now open to innovativeness and changE.The correct alternative
Hypothesis is

A) $p > 0.15$
B) $\mu > 0.15$
C) $p = 0.15$
D) $p < 0.15$
E) $\mu \neq 0.15$

Question 11

A large software development firm recently relocated its facilities.Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities.They believe that the firm's professionals volunteer an average of more than 15 hours per month.If this is not the case, they will institute an incentive program to increase community involvement.Based on data collected they perform the appropriate hypothesis test.A Type II error in this context means
I.They failed to detect that the average number of hours volunteered by the firm's professional employees is more than 15 hours when in fact it is.
II.They would decide not to institute an incentive program to increase community involvement when they should have.
III.They would waste money instituting an incentive program to increase community involvement among its professional employees that was not needed.

A)I only
B)II only
C)III only
D)Both I and II
E)Both I and III

Question 12

Insurance companies track life expectancy information to assist in determining the cost of life insurance policies.Last year the average life expectancy of all policyholders was 77 years.ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample some of their recently paid policies.The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than beforE.Which of the following statement is true about this hypothesis test?

A)It is a one tailed test about a mean.
B)It is a one tailed test about a proportion.
C)It is a two tailed test about a mean.
D)It is a two tailed test about a proportion.
E)None of these.

Question 13

In the past, the mean running time for a certain type of flashlight battery has been 8.4 hours.
The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result.The hypotheses are:
$H _ { 0 } : \mu = 8.4$ hours
$H _ { A } : \mu > 8.4$ hours
Explain the result of a Type II error.

A)The manufacturer will decide the mean battery life is greater than 8.4 hours when in fact it is greater than 8.4 hours.
B)The manufacturer will decide the mean battery life is less than 8.4 hours when in fact it is greater than 8.4 hours.
C)The manufacturer will decide the mean battery life is 8.4 hours when in fact it is 8.4 hours.
D)The manufacturer will decide the mean battery life is 8.4 hours when in fact it is greater than 8.4 hours.
E)The manufacturer will decide the mean battery life is greater than 8.4 hours when in fact it is 8.4 hours.

Question 14

A large software development firm recently relocated its facilities.Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities.They believe that the firm's professionals volunteer an average of more than 15 hours per month.If this is not the case, they will institute an incentive program to increase community involvement.A random sample of 24 professionals yields a mean of 16.6 hours and a standard deviation of 2.22 hours.The P-value associated with the resulting test statistic is 0.0009.At ? = 0.05, which
Of the following is the correct conclusion?
I.We reject the null hypothesis.
II.We fail to reject the null hypothesis.
III.The firm shouldn't need to institute an incentive program because the evidence indicates
That professional employees volunteer an average of more than 15 hours per month in
Their local community.

A)I only
B)Both II and III
C)Both I and III
D)III only
E)II only

Question 15

In the past, the mean running time for a certain type of flashlight battery has been 8.3 hours.
The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result.The hypotheses are:
$H _ { 0 } : \mu = 8.3$ hours
$H _ { A } : \mu > 8.3$ hours
Explain the result of a Type I error.

A)The manufacturer will decide the mean battery life is less than 8.3 hours when in fact it is greater than 8.3 hours.
B)The manufacturer will decide the mean battery life is greater than 8.3 hours when in fact it is less than 8.3 hours.
C)The manufacturer will decide the mean battery life is greater than 8.3 hours when in fact it is greater than 8.3 hours.
D)The manufacturer will decide the mean battery life is 8.3 hours when in fact it is greater than 8.3 hours.
E)The manufacturer will decide the mean battery life is greater than 8.3 hours when in fact it is 8.3 hours.

Question 16

Insurance companies track life expectancy information to assist in determining the cost of life insurance policies.Last year the average life expectancy of all policyholders was 77 years.ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample 20 of their recently paid policies.The sample has a mean of 78.6 years and a standard deviation of 4.48 years.The P-value associated with the resulting test statistic is 0.063.At ? = 0.05, which of the following is the correct conclusion?
I.We fail to reject the null hypothesis.
II.We reject the null hypothesis.
III.There is not significant evidence to indicate an increase in average life expectancy.

A)I only
B)II only
C)III only
D)Both I and III
E)Both II and III

Question 17

Which of the following would increase the power of a test?
I)Increase the sample size
II)Decrease the significance level
III)Increase alpha

A)I only
B)II only
C)III only
D)I and II
E)I and III

Question 18

The average diastolic blood pressure of a group of men suffering from high blood pressure is 97 mmHg.During a clinical trial, the men receive a medication which it is hoped will lower their blood pressure.After three months, the researcher wants to perform a hypothesis test to determine whether the average diastolic blood pressure of the men has decreased.The
Hypotheses are: $$\begin{array} { l } H _ { 0 } : \mu = 97 \mathrm { mmHg } \\H _ { A } : \mu < 97 \mathrm { mmHg }\end{array}$$
Explain the result of a Type II error.

A)The researcher will conclude that the average diastolic blood pressure of the men is the same when in fact it has decreased.
B)The researcher will conclude that the average diastolic blood pressure of the men is the same when in fact it is the same.
C)The researcher will conclude that the average diastolic blood pressure of the men has increased when in fact it has decreased.
D)The researcher will conclude that the average diastolic blood pressure of the men has decreased when in fact it has increased.
E)The researcher will conclude that the average diastolic blood pressure of the men has decreased when in fact it is the same.

Question 19

A psychologist claims that more than 2.2% of the population suffers from professional problems due to extreme shyness.Identify the Type II in this context.

A)The error of accepting the claim that the true proportion is more than 2.2% when it really is more than 2.2%.
B)The error of rejecting the claim that the true proportion is more than 2.2% when it really is more than 2.2%.
C)The error of rejecting the claim that the true proportion is at most 2.2% when it really is at most 2.2%.
D)The error of failing to reject the claim that the true proportion is at most 2.2% when it is actually more than 2.2%.
E)The error of failing to accept the claim that the true proportion is at most 2.2% when it is actually more than 2.2%.

Question 20

In 1990, the average math SAT score for students at one school was 490.Five years later, a teacher wants to perform a hypothesis test to determine whether the average SAT score of students at the school has changed from the 1990 mean of 490.The hypotheses are: $$\begin{array} { l } H _ { 0 } : \mu = 490 \\H _ { A } : \mu \neq 490\end{array}$$
Explain the result of a Type II error.

A)The teacher will conclude that the mean math SAT score at the school is the same when in fact it is the same.
B)The teacher will conclude that the mean math SAT score at the school has increased when in fact it is the same.
C)The teacher will conclude that the mean math SAT score at the school is different when in fact it is the same.
D)The teacher will conclude that the mean math SAT score at the school has decreased when in fact it is the same.
E)The teacher will conclude that the mean math SAT score at the school is the same when in fact it is different