Deck 9: Hypothesis Testing

Question 1

In the past, the mean running time for a certain type of flashlight battery has been 8.0 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: $$\begin{array} { l } \mathrm { H } _ { 0 } : \mu = 8.0 \text { hours } \\\mathrm { H } _ { \mathrm { a } } : \mu > 8.0 \text { hours }\end{array}$$
Explain the meaning of a Type II error.

A) Concluding that $\mu > 8.0$ hours when in fact $\mu > 8.0$ hours
B) Failing to reject the hypothesis that $\mu = 8.0$ hours when in fact $\mu > 8.0$ hours
C) Concluding that $\mu > 8.0$ hours
D) Failing to reject the hypothesis that $\mu = 8.0$ hours when in fact $\mu = 8.0$ hours 110

Answer 1

Failing to reject the hypothesis that $\mu = 8.0$ hours when in fact $\mu > 8.0$ hours

Question 2

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 1 in every ten thousand. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the
Results of the test apply.

A) Any sample of Americans
B) Any sample of Americans claiming to have seen a UFO
C) All Americans claiming to have seen a UFO
D) All Americans

Answer 2

All Americans

Question 3

A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis?

A) Greater than or equal to 0.10
B) Less than or equal to 0.05
C) Less than or equal to 0.10
D) Greater than or equal to 0.05
E) Less than or equal to 0.025

Answer 3

B

Question 4

The owner of a football team claims that the average attendance at home games is over 4000, and he is therefore justified in moving the team to a city with a larger stadium. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis.
Identify the population to which the results of the test apply.

A) All games played by the team in question in which the attendance is over 4000
B) All future home games to be played by the team in question
C) All home games played by the team in question
D) None of the populations given are appropriate.

Question 5

A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the conclusion of the hypothesis test assuming that the results of the sampling lead to rejection of the null hypothesis.

A) Conclusion: Support the claim that the mean is equal to 16 ounces.
B) Conclusion: Support the claim that the mean is greater than 16 ounces.
C) Conclusion: Support the claim that the mean is not equal to 16 ounces.
D) Conclusion: Support the claim that the mean is less than 16 ounces.

Question 6

A consumer group claims that the mean running time for a certain type of flashlight battery is not the same as the manufacturer's claims. Determine the null and alternative hypotheses for the test
Described.

A) $\mathrm{H}_{0}: \mu=$ Manufacturer's claims
$\mathrm{H}_{\mathrm{a}}: \mu<$ Manufacturer's claims

B) $\mathrm{H}_{0}: \mu=$ Manufacturer's claims
$\mathrm{H}_{\mathrm{a}}: \mu \neq$ Manufacturer's claims


C) $\mathrm{H}_{0}: \mu=$ Manufacturer's claims
$\mathrm{H}_{\mathrm{a}}: \mu>$ Manufacturer's claims


D) $\mathrm{H}_{0}: \mu \neq$ Manufacturer's claims
$\mathrm{H}_{\mathrm{a}}: \mu=$ Manufacturer's claims

Question 7

$\mathrm { H } _ { \mathrm { a } } : \mu > 19.9 , \bar { x } = 23.1 , \sigma = 8 , \mathrm { n } = 100$ . Without computing a $\mathrm { P }$ -value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.

A) $\mathrm { H } _ { \mathrm { a } }$ is not supported : $\bar { x }$ is more than 3 standard deviations above the claimed mean.
B) $\mathrm { H } _ { \mathrm { a } }$ is not supported: $\bar { x }$ is less than 1 standard deviation above the claimed mean.
C) $\mathrm { H } _ { \mathrm { a } }$ is supported ; $\bar { x }$ is more than 3 standard deviations above the claimed mean.
D) $\mathrm { H } _ { \mathrm { a } }$ is supported : $\bar { x }$ is less than 1 standard deviation above the claimed mean.

Question 8

A study of a brand of "in the shell peanuts" gives the following results: $$\begin{array} { c | c } \begin{array} { l } \text { Number of } \\\text { Peanuts per bag }\end{array} & \text { Probability } \\\hline 25 & 0.006 \\30 & 0.020 \\35 & 0.093 \\40 & 0.150 \\45 & 0.350 \\50 & 0.217 \\55 & 0.170\end{array}$$ If a fan purchased a bag with 30 peanuts, what is the lowest level at which this would be a significant event?

A) 0.05
B) 0.025
C) 0.01
D) It is not significant at any of the levels given.

Question 9

In the past, the mean running time for a certain type of flashlight battery has been 9.8 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:
$\mathrm { H } _ { 0 } : \mu = 9.8$ hours
$\mathrm { H } _ { \mathrm { a } } : \mu > 9.8 \text { hours }$
Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running time has not increased.

A) Type I error
B) Type II error
C) Correct decision

Question 10

A nationwide study of American homeowners revealed that 65% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in omaha. Find the P-value for a test of the claim that the proportion with lawn mowers in Omaha is higher than 65%. Among 497 randomly selected homes in Omaha, 340 had one or more lawn
Mowers. Use Table 5.1 to find the best answer.

A) 0.0559
B) 0.1118
C) 0.0252
D) 0.0505

Question 11

A two-tailed test is conducted at the 5% significance level. What is the right tail percentile required to reject the null hypothesis?

A) 10%
B) 5%
C) 2.5%
D) 95%
E) 97.5%

Question 12

A supplier of DVDs claims that no more than 1% of the DVDs are defective. In a random sample of 600 DVDs, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. At the 0.01 level of significance, test the supplier's claim that no more than 1% are defective.

A) Do not reject the null hypothesis and conclude that there is evidence to support the claim that more than 1% of the DVDs are defective.
B) Reject the null hypothesis and conclude that there is insufficient evidence to support the claim that more than 1% of the DVDs are defective.
C) Do not reject the null hypothesis and conclude that there is insufficient evidence to support the claim that more than 1% of the DVDs are defective.
D) Reject the null hypothesis and conclude that there is sufficient evidence to support the claim that more than 1% of the DVDs are defective.

Question 13

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 1 in every one thousand. State the null hypothesis and the alternative hypothesis for a test of Significance.

A) $\mathrm{H}_{0}: \mathrm{p}=0.001$
$\mathrm{H}_{\mathrm{a}}: \mathrm{p}>0.001$

B) $\mathrm{H}_{0}: \mathrm{p}=0.001$
$\mathrm{H}_{\mathrm{a}}: \mathrm{p}<0.001$

C) $\mathrm{H}_{0}: \mathrm{p}>0.001$
$\mathrm{H}_{\mathrm{a}}: \mathrm{p}=0.001$

D) $\mathrm{H}_{0}: \mathrm{p}<0.001$
$\mathrm{H}_{\mathrm{a}}: \mathrm{p}=0.001$

Question 14

In 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes.
The hypotheses are: $$\begin{array}{l}\mathrm{H}_{0}: \mu=9.4 \text { minutes } \\\mathrm{H}_{\mathrm{a}}: \mu \neq 9.4 \text { minutes }\end{array}$$
Explain the meaning of a correct decision.

A) Failing to reject the hypothesis that $\mu=9.4$ minutes when in fact $\mu=9.4$ minutes OR concluding that $\mu>9.4$ minutes when in fact $\mu>9.4$ minutes
B) Failing to reject the hypothesis that $\mu=9.4$ minutes when in fact $\mu=9.4$ minutes OR concluding that $\mu \neq 9.4$ minutes when in fact $\mu \neq 9.4$ minutes
C) Failing to reject the hypothesis that $\mu=9.4$ minutes when in fact $\mu \neq 9.4$ minutes
D) Concluding that $\mu \neq 9.4$ minutes when in fact $\mu=9.4$ minutes

Question 15

$$\mathrm { z } = 1.8 \text { for } \mathrm { H } _ { \mathrm { a } } : \mu > \text { claimed value. What is the P-value for the test? }$$

A) 0.9641
B) 3.59
C) 96.41
D) 0.0359
E) None of the above

Question 16

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a mean different from the 600 mg claimed by the manufacturer. Test this claim at the 0.02 level of significance. The mean acetaminophen content for a random sample of n = 41 tablets is 603.3 mg.
Assume that the population standard deviation is 4.9 mg.

A) Since the test statistic is greater than the critical z, there is sufficient evidence to accept the null hypothesis and to support the claim that the mean content of acetaminophen is 600 mg.
B) Since the test statistic is greater than the critical z, there is sufficient evidence to reject the null hypothesis and to support the claim that the mean content of acetaminophen is not 600 mg.
C) Since the test statistic is less than the critical z, there is sufficient evidence to reject the null hypothesis and to support the claim that the mean content of acetaminophen is not 600 mg.
D) Since the test statistic is greater than the critical z, there is insufficient evidence to reject the null hypothesis and to support the claim that the mean content of acetaminophen is not 600 mg.

Question 17

The owner of a football team claims that the average attendance at home games is over 3000, 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 non-technical terms.

A) There is sufficient evidence to support the claim that the mean attendance is greater than 3000.
B) There is sufficient evidence to support the claim that the mean attendance is equal to 3000.
C) There is not sufficient evidence to support the claim that the mean attendance is greater than 3000.
D) There is not sufficient evidence to support the claim that the mean attendance is less than 3000.

Question 18

In 1990, the average duration of long-distance telephone calls originating in one town was $9.4$ minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of $9.4$ minutes. The mean duration for a random sample of 50 calls originating in the town was $8.6$ minutes. Does the data provide sufficient evidence to conclude that the mean call duration, $\mu$ , is different from the 1990 mean of $9.4$ minutes? Perform the appropriate hypothesis test using a significance level of $0.01$ . Assume that $\sigma=4.8$ minutes.

A) With a $z$ of $-1.2$ there is sufficient eridence to conclude that the mean value has changed from the 1990 mean of $9.4$ minutes.
B) With a P-value of $0.2302$ there is not sufficient evidence to conclude that the mean value is less than the 1990 mean of $9.4$ minutes.
C) With a P-value of $0.2302$ there is sufficient evidence to conclude that the mean value is less than the 1990 mean of $9.4$ minutes.
D) With a $z$ of $-1.2$ there is not sufficient evidence to conclude that the mean value has changed from the 1990 mean of $9.4$ minutes.

Question 19

A right-tailed test is conducted at the 5% significance level. Which of the following z-scores is the smallest one in absolute value that leads to rejection of the null hypothesis?

A) 1.61
B) 1.85
C) -1.98
D) -2.06

Question 20

At one school, the mean amount of time that tenth-graders spend watching television each week is 18.4 hours. The principal introduces a campaign to encourage the students to watch less television.
One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased. Formulate the null and alternative hypotheses for the study described.

A) $\mathrm { H } _ { 0 } : \mu = 18.4$ hours
$\mathrm { H } _ { \alpha } : \mu \neq 18.4$ hours

B) $H _ { 0 } : \mu = 18.4$ hours
$\mathrm { H } _ { \alpha } : \mu < 18.4$ hours

C) $\mathrm { H } _ { 0 } : \mu \geq 18.4$ hours
$\mathrm { H } _ { \alpha } : \mu < 18.4$ hours

D) $\mathrm { H } _ { 0 } : \mu = 18.4$ hours
$\mathrm { H } _ { \alpha } : \mu > 18.4$ hours

Question 21

A long-distance telephone company claims that the mean duration of long-distance telephone calls originating in one town was greater than 9.4 minutes, which is the average for the state. Determine the conclusion of the hypothesis test assuming that the results of the sampling do not lead to rejection of the null hypothesis.

A) Conclusion: Support the claim that the mean is less than 9.4 minutes.
B) Conclusion: Support the claim that the mean is greater than 9.4 minutes.
C) Conclusion: Support the claim that the mean is equal to 9.4 minutes.
D) Conclusion: Do not support the claim that the mean is greater than 9.4 minutes.

Question 22

A poll of 1068 adult Americans reveals that 52% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 significance level, test the claim that more than half of all voters prefer the Democrat.

A) Reject the null hypothesis. Conclude that there is insufficient evidence that more than half of all voters prefer Democrats.
B) Do not reject the null hypothesis. Conclude that there is sufficient evidence that more than half of all voters prefer Democrats.
C) Reject the null hypothesis. Conclude that there is sufficient evidence that more than half of all voters prefer Democrats.
D) Do not reject the null hypothesis. Conclude that there is insufficient evidence that more than half of all voters prefer Democrats.

Question 23

$\mathrm{H}_{\mathrm{a}}: \mu>21.1, \bar{x}=21.5, \sigma=6, \mathrm{n}=100$ ; Without computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.

A) $\mathrm{H}_{\mathrm{a}}$ is supported; $\bar{x}$ is less than 1 standard deviation above the claimed mean.
B) $\mathrm{H}_{\mathrm{a}}$ is supported; $\bar{x}$ is more than 4 standard deviations above the claimed mean.
C) $\mathrm{H}_{\mathrm{a}}$ is not supported; $\bar{x}$ is less than 1 standard deviation above the claimed mean.
D) $\mathrm{H}_{8}$ is not supported; $\bar{x}$ is more than 4 standard deviations above the claimed mean.

Question 24

A two-tailed test is conducted at the 5% significance level. What is the left tail percentile required to reject the null hypothesis?

A) 10%
B) 5%
C) 2.5%
D) 95%
E) 97.5%

Question 25

A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the null and alternative hypotheses for the test
Described.

A) $\mathrm{H}_{0}: \mu=16$ ounces
$\mathrm{H}_{\mathrm{a}}: \mu<16$ ounces

B) $\mathrm{H}_{0}: \mu \neq 16$ ounces
$\mathrm{H}_{\mathrm{a}}: \mu=16$ ounces

C) $\mathrm{H}_{0}: \mu=16$ ounces
$\mathrm{H}_{\mathrm{a}}: \mu>16$ ounces

D) $\mathrm{H}_{0}: \mu=16$ ounces
$\mathrm{H}_{\mathrm{a}}: \mu \neq 16$ ounces

Question 26

A study of a brand of "in the shell peanuts" gives the following results: $$\begin{array} { c | r } \begin{array} { l } \text { Number of } \\\text { Peanuts per bag }\end{array} & \text { Probability } \\\hline 25 & 0.003 \\30 & 0.020 \\35 & 0.090 \\40 & 0.150 \\45 & 0.350 \\50 & 0.217 \\55 & 0.170\end{array}$$ A significant event at the 0.01 level is a fan getting a bag with how many peanuts?

A) 30 peanuts
B) 25 or 30 peanuts
C) 25 or 55 peanuts
D) 25 peanuts

Question 27

$$\mathrm { z } = 0.5 \text { for } \mathrm { H } _ { \mathrm { a } } : \mu < \text { claimed value. What is the } \mathrm { P } \text {-value for the test? }$$

A) 30.85
B) 69.15
C) 0.6915
D) 0.3085
E) None of the above

Question 28

A two-tailed test is conducted at the 0.10 significance level. What is the P-value required to reject the null hypothesis?

A) Greater than or equal to .010
B) Greater than or equal to 0.05
C) Less than or equal to 0.20
D) Less than or equal to 0.05
E) Less than or equal to 0.10

Question 29

An airline claims that the no-show rate for passengers booked on its flights is less than 6%. Of 380 randomly selected reservations, 18 were no-shows. Use Table 5.1 to find the best estimate of the P- value for a test of the airline's claim.

A) 0.0746
B) 0.1492
C) 0.3508
D) 0.1230

Question 30

In 1990, the average math SAT score for students at one school was 495. 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 495. The hypotheses are: $$\begin{array} { l } \mathrm { H } _ { 0 } : \mu = 495 \\\mathrm { H } _ { \mathrm { a } } : \mu \neq 495\end{array}$$
Explain the meaning of a Type II error.

A) Concluding that $\mu \neq 495$ minutes when in fact $\mu = 495$
B) Failing to reject the hypothesis that $\mu = 495$ when in fact $\mu = 495$
C) Failing to reject the hypothesis that $\mu = 495$ when in fact $\mu \neq 495$
D) Concluding that $\mu > 495$ when in fact $\mu = 495$

Question 31

At one school, the average amount of time that tenth-graders spend watching television each week is 21.6 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average
Amount of time spent watching television per week has decreased. The hypotheses are:
$\begin{array}{l}\mathrm{H}_{0}: \mu=21.6 \text { hours } \\\mathrm{H}_{\mathrm{a}}: \mu<21.6 \text { hours }\end{array}$
Explain the meaning of a correct decision.

A) Failing to reject the hypothesis that $\mu=21.6$ hours when in fact $\mu=21.6$ hours OR concluding that $\mu<21.6$ hours when in fact $\mu<21.6$ hours
B) Concluding that $\mu>21.6$ hours when in fact $\mu<21.6$ hours
C) Failing to reject the hypothesis that $\mu=21.6$ hours when in fact $\mu<21.6$ hours
D) Concluding that $\mu<21.6$ hours when in fact $\mu=21.6$ hours

Question 32

A psychologist claims that more than 19 percent of the population suffers from professional problems due to extreme shyness. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of
The test apply.

A) The population is all shy workers.
B) The population cannot be identified from the description of the study.
C) The population is all American workers.
D) The population is all American professional workers (doctors, lawyers, CPA's, and the like).

Question 33

The principal of a middle school claims that annual incomes of the families of the seventh-graders at his school vary more than the annual incomes of the families of the seventh-graders at a neighboring school, which have variation described by $\sigma = \$ 13,700$ . Assume that a hypothesis test of the claim has
Been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.

A) The current seventh graders at the principal's school
B) Seventh graders' families at the school with a standard deviation of $13,700
C) All of the families of the class of seventh graders at the principal's school
D) All seventh graders' families

Question 34

In 1990, the average duration of long-distance telephone calls originating in one town was 9.3 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.3 minutes.
Formulate the null and alternative hypotheses for the study described.

A) $\mathrm{H}_{0}: \mu=9.3$ minutes
$\mathrm{H}_{\alpha}: \mu<9.3$ minutes

B) $\mathrm{H}_{0}: \mu=9.3$ minutes
$\mathrm{H}_{\alpha}: \mu>9.3$ minutes

C) $\mathrm{H}_{0}: \mu=9.3$ minutes
$\mathrm{H}_{\alpha}: \mu \neq 9.3$ minutes

D) $\mathrm{H}_{0}: \mu \neq 9.3$ minutes
$\mathrm{H}_{\alpha}: \mu=9.3$ minutes

Question 35

A manufacturer claims that the mean amount of juice in its 16 ounce bottles is $16.1$ ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The mean volume of juice for a random sample of 70 bottles was $15.94$ ounces. Do the data provide sufficient evidence to conclude that the mean amount of juice for all 16ounce bottles, $\mu$ , is less than $16.1$ ounces? Perform the appropriate hypothesis test using a significance level of $0.10$ . Assume that $\sigma=0.9$ ounces.

A) The $z$ of $-1.49$ provides sufficient evidence to conclude that the mean amount of juice is less than $16.1 \mathrm{oz}$ .
B) The $z$ of $-1.49$ does not provide sufficient evidence to conclude that the mean amount of juice is less than $16.1 \mathrm{oz}$ .

C) The $z$ of $-0.1778$ does not provide sufficient evidence to conclude that the mean amount of juice is less than $16.1 \mathrm{oz}$ .
D) The $z$ of $-0.1778$ provides sufficient evidence to conclude that the mean amount of juice is less than $16.1 \mathrm{oz}$ . 113

Question 36

A two-tailed test is conducted at the 5% significance level. Which of the z-scores below is the smallest one that leads to rejection of the null hypothesis?

A) 1.12
B) 1.48
C) 1.84
D) 2.15

Question 37

A psychologist claims that more than 29 percent of the professional population suffers from problems due to extreme shyness. 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 non-technical terms.

A) There is sufficient evidence to support the claim that the true proportion is less than 29 percent.
B) There is not sufficient evidence to support the claim that the true proportion is greater than 29 percent.
C) There is sufficient evidence to support the claim that the true proportion is equal to 29 percent.
D) There is sufficient evidence to support the claim that the true proportion is greater than 29 percent.

Question 38

A researcher wants to check the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 35 such cases from court files and finds that $\bar{x}$ = 16.7 months. Assume that the population standard deviation is 7 months. Test the null hypothesis that µ = 18.7 at the 0.05 significance level.

A) Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported.
B) Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported.
C) Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported.
D) Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported.

Question 39

A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The hypotheses are:
$\mathrm{H}_{0}: \mu=16.1$ ounces
$\mathrm{H}_{\mathrm{a}}: \mu<16.1 \text { ounces }$
Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean amount of juice, ?, is less than 16.1 ounces.

A) Type II error
B) Correct decision
C) Type I error

Question 40

The owner of a football team claims that the mean attendance at games is greater than 83,900. State the null hypothesis and the alternative hypothesis for a test of significance.

A) $\mathrm{H}_{0}: \mu>83,900$
$\mathrm{H}_{\mathrm{a}}: \mu=83,900$

B) $\mathrm{H}_{0}: \mu<83,900$
$\mathrm{H}_{\mathrm{a}}: \mu=83,900$

C) $\mathrm{H}_{0}: \mu=83,900$
$\mathrm{H}_{\mathrm{a}}: \mu>83,900$

D) $\mathrm{H}_{0}: \mu=83,900$
$\mathrm{H}_{\mathrm{a}}: \mu<83,900$

Question 41

The standard score for a two-tailed test is 2.0. What is the P-value?

A) 0.9772
B) 0.0456
C) 0.0228
D) 97.72

Question 42

$\mathrm{H}_{\mathrm{a}}: \mu>19, \bar{x}=23.8, \sigma=8, \mathrm{n}=100$ ; without computing a $\mathrm{P}$ -value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.

A) $\mathrm{H}_{\mathrm{a}}$ is not supported; $\bar{x}$ is less than 1 standard deviation above the claimed mean.
B) $\mathrm{H}_{\mathrm{a}}$ is not supported; $\bar{x}$ is more than 4 standard deriations above the claimed mean.
C) $\mathrm{H}_{a}$ is supported; $\bar{x}$ is less than 1 standard deviation above the claimed mean.
D) $\mathrm{H}_{\mathrm{a}}$ is supported; $\bar{x}$ is more than 4 standard deviations above the claimed mean.

Question 43

The average diastolic blood pressure of a group of men suffering from high blood pressure is 96 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: $$\begin{array}{l}\mathrm{H}_{0}: \mu=96 \mathrm{mmHg} \\\mathrm{H}_{\mathrm{a}}: \mu<96 \mathrm{mmHg}\end{array}$$
Explain the meaning of a Type II error.

A) Concluding that $\mu>96 \mathrm{mmHg}$ when in fact $\mu<96 \mathrm{mmHg}$
B) Failing to reject the hypothesis that $\mu=96 \mathrm{mmHg}$ when in fact $\mu<96 \mathrm{mmHg}$
C) Failing to reject the hypothesis that $\mu=96 \mathrm{mmHg}$ when in fact $\mu=96 \mathrm{mmHg}$
D) Concluding that $\mu<96 \mathrm{mmHg}$ when in fact $\mu=96 \mathrm{mmHg}$

Question 44

A two-tailed test is conducted at the 5% significance level. What is the smallest z-score listed below that results in rejection of the null hypothesis?

A) 1.17
B) 1.58
C) 1.81
D) 2.89

Question 45

A researcher claims that more than 62% of voters favor gun control. State the null hypothesis and the alternative hypothesis for a test of significance.

A) $\mathrm { H } _ { 0 } : \mathrm { p } > 0.62$
$\mathrm { H } _ { \mathrm { a } } : \mathrm { p } = 0.62$

B) $\mathrm { H } _ { 0 } : \mathrm { p } < 0.62$
$H _ { a } : p = 0.62$

C) $\mathrm { H } _ { 0 } : \mathrm { p } = 0.62$
$\mathrm { H } _ { \mathrm { a } } : \mathrm { p } > 0.62$

D) $\mathrm { H } _ { 0 } : \mathrm { p } = 0.62$
$\mathrm { H } _ { \mathrm { a } } : \mathrm { p } < 0.62$

Question 46

At one school, the average amount of time that tenth-graders spend watching television each week is 21 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased. The hypotheses are: $$\begin{array} { l } \mathrm { H } _ { 0 } : \mu = 21 \text { hours } \\\mathrm { H } _ { \mathrm { a } } : \mu < 21 \text { hours }\end{array}$$ Suppose that the results of the sampling lead to non-rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean amount of time, ?, spent watching television has increased.

A) Type I error
B) Correct decision
C) Type II error

Question 47

A cereal company claims that the mean weight of the cereal in its 14 oz. packets is at least 14 oz. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.

A) The cereal packets that were tested
B) The cereal packets of one kind manufactured by the cereal company
C) All 14 oz. cereal packets used by the cereal company
D) All cereal packets manufactured by the cereal company

Question 48

A study of a brand of "in the shell peanuts" gives the following results: $$\begin{array} { c | c } \begin{array} { l } \text { Number of } \\\text { Peanuts per bag }\end{array} & \text { Probability } \\\hline 25 & 0.003 \\30 & 0.020 \\35 & 0.090 \\40 & 0.150 \\45 & 0.450 \\50 & 0.217 \\55 & 0.070\end{array}$$ A significant event at the 0.10 level is a fan getting a bag with how many peanuts?

A) 25 or 30 or 35 peanuts
B) 25 or 55 peanuts
C) 35 or 45 or 50 peanuts
D) None of the selections are correct.

Question 49

In 1990 , the average duration of long-distance telephone calls originating in one town was $9.4$ minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of $9.4$ minutes. The mean duration for a random sample of 50 calls originating in the town was $8.6$ minutes. Does the data provide sufficient evidence to conclude that the mean call duration, $\mu$ , has changed from the 1990 mean of $9.4$ minutes? Perform the appropriate hypothesis test using a significance level of $0.01$ . Assume that $\sigma=4.2$ minutes.

A) Since the P-value is greater than the significance level, the data provide sufficient evidence to accept the null hypothesis and conclude that the mean call duration has changed.
B) Since the P-value is less than the significance level, the data provide sufficient evidence to reject the null hypothesis and conclude that the mean call duration has changed.
C) Since the P-value is greater than the significance level, the data provide insufficient evidence to reject the null hypothesis and conclude that the mean call duration has changed.
D) Since the P-value is greater than the significance level, the data provide sufficient evidence to reject the null hypothesis and conclude that the mean call duration has changed.

Question 50

In 1990, the average math SAT score for students at one school was 510. 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 510. Formulate the null and alternative hypotheses for the study described.

A) $\mathrm { H } _ { 0 } : \mu = 510$
$\mathrm { H } _ { \alpha } : \mu > 510$

B) $\mathrm { H } _ { 0 } : \mu = 510$
$\mathrm { H } _ { \alpha } : \mu < 510$

C) $\mathrm { H } _ { 0 } : \mu = 510$
$\mathrm { H } _ { \alpha } : \mu \neq 510$

D) $\mathrm { H } _ { 0 } : \mu \geq 510$
$\mathrm { H } _ { \alpha } : \mu < 510$

Question 51

The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, µ, of 45ºF, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims that the true mean temperature is incorrect. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.

A) All refrigerators produced by the manufacturer specifically to cool kegs of a particular German pilsner beer
B) All refrigerators produced by the manufacturer
C) All refrigerators produced by the manufacturer specifically to cool kegs of beer
D) There is not sufficient description to identify the population.

Question 52

A two-tailed test is conducted at the 10% significance level. What is the z-score closest to zero in the list that will result in rejection of the null hypothesis?

A) 1.19
B) -1.54
C) -1.84
D) 2.59

Question 53

A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer wants to perform a hypothesis test to determine whether their suspicion is correct. The mean fee charged by the clinic for a random sample of 65 patients receiving this procedure was $1280. Do the data provide sufficient evidence to conclude that the mean fee charged by this particular clinic is higher than $1200? Perform the appropriate hypothesis test using a significance level of 0.01. Assume that ? = $220.

A) The z-score of 2.93 provides sufficient evidence to conclude that the mean fee charged by this clinic for the medical procedure is greater than $1200.
B) The z-score of 0.363 does not provide sufficient evidence to conclude that the mean fee charged by this clinic for the medical procedure is greater than $1200.
C) The P-value of .363 does not provide sufficient evidence to conclude that the mean fee charged by this clinic for the medical procedure is greater than $1200.
D) The P-value of .045 provides sufficient evidence to conclude that the mean fee charged by this clinic for the medical procedure is greater than $1200.

Question 54

A long-distance telephone company claims that the mean duration of long-distance telephone calls originating in one town was not equal to 9.4 minutes, which is the average for the state. Determine The null and alternative hypotheses for the test described.

A) $\mathrm{H}_{0}: \mu=9.4$ minute long-distance telephone call in the town $\mathrm{H}_{\mathrm{a}}: \mu>9.4$ minute long-distance telephone call in the town
B) $\mathrm{H}_{0}: \mu \neq 9.4$ minute long-distance telephone call in the town $\mathrm{H}_{\mathrm{a}}: \mu=9.4$ minute long-distance telephone call in the town
C) $\mathrm{H}_{0}: \mu=9.4$ minute long-distance telephone call in the town $\mathrm{H}_{\mathrm{a}}: \mu \neq 9.4$ minute long-distance telephone call in the town
D) $\mathrm{H}_{0}: \mu=9.4$ minute long-distance telephone call in the town $\mathrm{H}_{\mathrm{a}}: \mu<9.4$ minute long-distance telephone call in the town

Question 55

$\mathrm{z}=-1.5 \text { for } \mathrm{H}_{\mathrm{a}}: \mu \neq \text {claimed value; What is the P-value for the test? }$

A) 0.0668
B) 0.1336
C) 0.8664
D) 0.9332
E) None of the above

Question 56

A random sample of 139 forty-year-old men contains 26% smokers. Use Table 5.1 to estimate the P- value for a test of the claim that the percentage of forty-year-old men that smoke is 22%.

A) 0.2542
B) 0.1401
C) 0.2802
D) 0.1271

Question 57

The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, µ, of 46ºF, 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. 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 non-technical terms.

A) The brewery owner has proved his case.
B) There is sufficient evidence to support the claim that the mean temperature is equal to 46ºF.
C) There is not sufficient evidence to support the claim that the mean temperature is different from 46ºF.
D) There is sufficient evidence to support the claim that the mean temperature is different from 46ºF.

Question 58

According to a recent poll 53% of Americans would vote for the incumbent president. If a random sample of 100 people results in 45% who would vote for the incumbent, test the hypothesis that the actual percentage is 53%. Use a 0.10 significance level and a two-tailed test.

A) Do not reject the null hypothesis. There is insufficient evidence to reject the claim that 53% of Americans would vote for the incumbent president.
B) Do not reject the null hypothesis. There is sufficient evidence to support the claim that 53% of Americans would vote for the incumbent president.
C) Reject the null hypothesis. There is sufficient evidence to reject the claim that 53% of Americans would vote for the incumbent president.
D) Reject the null hypothesis. There is insufficient evidence to support the claim that 53% of Americans would vote for the incumbent president.

Question 59

A manufacturer wishes to test the claim that one of its pancake mixes has a mean weight that does not equal 24 ounces as advertised. Determine the conclusion of the hypothesis test assuming that the results of the sampling lead to rejection of the null hypothesis.

A) Conclusion: Support the claim that the mean is greater than 24 ounces.
B) Conclusion: Support the claim that the mean is not equal to 24 ounces.
C) Conclusion: Support the claim that the mean is equal to 24 ounces.
D) Conclusion: Support the claim that the mean is less than 24 ounces.

Question 60

A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer wants to perform a hypothesis test to determine whether their suspicion is correct. The hypotheses are: $$\begin{array}{l}\mathrm{H}_{0}: \mu=\$ 1200 \\\mathrm{H}_{\mathrm{a}}: \mu>\$ 1200\end{array}$$
Explain the meaning of a correct decision.

A) Concluding that $\mu>\$ 1200$ when in fact $\mu=\$ 1200$
B) Concluding that $\mu<\$ 1200$ when in fact $\mu<\$ 1200$
C) Failing to reject the hypothesis that $\mu=\$ 1200$ when in fact $\mu>\$ 1200$
D) Failing to reject the hypothesis that $\mu=\$ 1200$ when in fact $\mu=\$ 1200$ OR concluding that $\mu>$ $\$ 1200$ when in fact $\mu>\$ 1200$