# A researcher claims that the amounts - Expert Answers

1

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.

2

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 3

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 4

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 s = $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 5

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 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 6

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

A. 97.5%

B. 5%

C. 2.5%

D. 95%

Question 7

A poll of 1,068 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 8

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

Question 9

A study of a brand of “in the shell peanuts” gives the following results:

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 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

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:

H0 : µ = 8.0 hours

Ha : µ 8.0 hours

Explain the meaning of a Type II error.

A. Concluding that µ 8.0 hours when in fact µ 8.0 hours

B. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ

8.0 hours

C. Concluding that µ 8.0 hours

D. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ = 8.0 hours

Question 12

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:

H0 : µ = 9.8 hours

Ha : µ 9.8 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

D. Can not be determined from this information

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.

H0: p = 0.001 Ha: p 0.001

H0: p = 0.001 Ha: p < 0.001

H0: p 0.001 Ha: p = 0.001

H0: p < 0.001 Ha: p = 0.001

Question 14

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 15

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 16

z = 1.8 for Ha: µ claimed value. What is the P-value for the test?

A. 0.9641

B. 3.59

C. 96.41

D. 0.0359

Question 17

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 18

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 19

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 20

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.

H0: µ = Manufacturer’s claims Ha: µ < Manufacturer’s claims

B.

H0: µ = Manufacturer’s claims Ha: µ ¹ Manufacturer’s claims

C.

H0: µ = Manufacturer’s claims Ha: µ Manufacturer’s claims

D.

H0: µ ¹ Manufacturer’s claims Ha: µ = Manufacturer’s claims

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.

2

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 3

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 4

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 s = $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 5

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 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 6

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

A. 97.5%

B. 5%

C. 2.5%

D. 95%

Question 7

A poll of 1,068 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 8

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

Question 9

A study of a brand of “in the shell peanuts” gives the following results:

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 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

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:

H0 : µ = 8.0 hours

Ha : µ 8.0 hours

Explain the meaning of a Type II error.

A. Concluding that µ 8.0 hours when in fact µ 8.0 hours

B. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ

8.0 hours

C. Concluding that µ 8.0 hours

D. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ = 8.0 hours

Question 12

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:

H0 : µ = 9.8 hours

Ha : µ 9.8 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

D. Can not be determined from this information

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.

H0: p = 0.001 Ha: p 0.001

H0: p = 0.001 Ha: p < 0.001

H0: p 0.001 Ha: p = 0.001

H0: p < 0.001 Ha: p = 0.001

Question 14

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 15

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 16

z = 1.8 for Ha: µ claimed value. What is the P-value for the test?

A. 0.9641

B. 3.59

C. 96.41

D. 0.0359

Question 17

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 18

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 19

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 20

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.

H0: µ = Manufacturer’s claims Ha: µ < Manufacturer’s claims

B.

H0: µ = Manufacturer’s claims Ha: µ ¹ Manufacturer’s claims

C.

H0: µ = Manufacturer’s claims Ha: µ Manufacturer’s claims

D.

H0: µ ¹ Manufacturer’s claims Ha: µ = Manufacturer’s claims

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