Stats homework - multiple choice

Question 1 of 40

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.Ho: µ = 18.4 hours H a : µ ¹ 18.4 hours

B.Ho: µ = 18.4 hours H a : µ < 18.4 hours

C.Ho: µ ³ 18.4 hours H a : µ < 18.4 hours

D.Ho: µ = 18.4 hours H a : µ > 18.4 hours

Question 2 of 40

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.H0: µ = 16 ounces Ha: µ < 16 ounces

B.H0: µ ¹ 16 ounces Ha: µ = 16 ounces

C.H0: µ = 16 ounces Ha: µ > 16 ounces

D.H0: µ = 16 ounces Ha: µ ¹ 16 ounces

Question 3 of 40

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, µ, is different from the 1990 mean of 9.4 minutes? Perform the appropriate hypothesis test using a significance level of 0.01. Assume that  = 4.8 minutes.

A. With a z of 1.2 there is sufficient evidence 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 4 of 40

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 of 40

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 0.10

D. Less than or equal to 0.05

Question 6 of 40

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 7 of 40

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 8 of 40

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 9 of 40

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 of 40

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 11 of 40

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 12 of 40

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 13 of 40

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 14 of 40

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 15 of 40

without computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.

A. is less than 1 standard deviation above the claimed mean.

B.is more than 4 standard deviations above the claimed mean.

C.is less than 1 standard deviation above the claimed mean.

D.is more than 4 standard deviations above the claimed mean.

Question 16 of 40

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 17 of 40

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.H0: p = 0.001 Ha: p > 0.001

B.H0: p = 0.001 Ha: p < 0.001

C.H0: p > 0.001 Ha: p = 0.001

D.H0: p < 0.001 Ha: p = 0.001

Question 18 of 40

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 19 of 40

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 20 of 40

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 21 of 40

2.5 Points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.

	Colorblind	Not Colorblind	Total
Male	8	52	60
Female	2	38	40
Total	10	90	100

If gender and colorblindness are independent, find the expected values corresponding to the four combinations of gender and colorblindness, and enter them in the following table along with row and column totals.

	Colorblind	Not Colorblind	Total
Male
Female
Total

 

A. Male Colorblind 6.0; Male Not Colorblind 54.0
B. Male Colorblind 7.0; Male Not Colorblind 53.0
C. Male Colorblind 8.0; Male Not Colorblind 52.0
D. Male Colorblind 6.0; Male Not Colorblind 53.0

Question 22 of 40

A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 24.8. What is the margin of error?

A. 4.4

B. 4.6

C. 4.8

D. 5.0

Question 23 of 40

A golfer wished to find a ball that would travel more than 160 yards when hit with his 7-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 8 times at the required speed. State the null and alternative hypotheses for this test.

A.H0: µ = 160; Ha: µ > 150

B.H0: µ = 150; Ha: µ > 150

C.H0: µ = 160; Ha: µ > 160

D.H0: µ = 140; Ha: µ > 160

Question 24 of 40

A golfer wished to find a ball that would travel more than 160 yards when hit with his 7-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 8 times at the required speed.

Data from this test resulted in a sample mean of 163.2 yards with a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer’s requirements. Use the partial t-table below to solve this problem.

Area in one tail

0.025 0.05

Area in two tails

Degrees of

Freedom

n - 1 0.05 0.10

6 2.447 1.943

7 2.365 1.895

8 2.306 1.860

9 2.262 1.833

A.Do not reject the null hypothesis. The data do not provide sufficient

evidence that the average distance is greater than 160 yards.

B. Reject the null hypothesis. The data does provide sufficient evidence that the average distance is greater than 160 yards.

C. t= 1.2334; Critical value = 1.992

D. Insufficient information to answer this question.

Question 25 of 40

2.5 Points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.

	Colorblind	Not Colorblind	Total
Male	7	53	60
Female	1	39	40
Total	8	92	100

Find the value of the χ2 statistic for the data above.

A. 1.325
B. 1.318
C. 1.286
D. 1.264

Question 26 of 40

A golfer wished to find a ball that would travel more than 180 yards when hit with his 5-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 7 times at the required speed.

	Area in one tail
	0.025	0.05
	Area in two tails
Degrees of Freedom n - 1	0.05	0.10
6	2.447	1.943
7	2.365	1.895
8	2.306	1.860
9	2.262	1.833

Data from this test resulted in a sample mean of 184.2 yards and a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer’s requirements. Use the partial t-table below.

Area in one tail

0.025 0.05

Area in two tails

Degrees of

Freedom

n - 1 0.05 0.10

6 2.447 1.943

7 2.365 1.895

8 2.306 1.860

9 2.262 1.833

A.Reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 180 yards.

B. Reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 180 yards.

C. Do not reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 180 yards.

D. Do not reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 180 yards.

Question 27 of 40

The margin of error in estimating the population mean of a normal population is E = 9.3 when the sample size is 15. If the sample size had been 18 and the sample standard deviation did not change, would the margin of error be larger or smaller than 9.3? Explain your answer.

A. Smaller. E decreases as the square root of the sample size gets larger.

B. Smaller. E increases as the square root of the sample size gets larger.

C. Larger. E decreases as the square root of the sample size gets larger.

D. Larger. E increases as the square root of the sample size gets larger.

Question 28 of 40

2.5 Points

The following data were analyzed using one-way analysis of variance.

A	B	C
34	27	19
26	23	21
31	29	22
28	21	12

Which one of the following statements is correct?

A. The purpose of the analysis is to determine whether the groups A, B, and C are independent.
B. The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal.
C. The purpose of the analysis is to test the hypothesis that the population variances of the three groups are equal.
D. The purpose of the analysis is to test the hypothesis that the sample means of the three groups are equal.

Question 29 of 40

2.5 Points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.

	Colorblind	Not Colorblind	Total
Male	8	52	60
Female	2	38	40
Total	10	90	100

Find the value of the χ2 statistic for the data above.

A. 1.463
B. 1.852
C. 1.947
D. 1.949

Question 30 of 40

Which of the following statements is true?

A. The p distribution cannot be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.

B. The t distribution can be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.

C. The t distribution cannot be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.

D. The p distribution can be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.

Question 31 of 40

2.5 Points

A golfer wished to find a ball that would travel more than 170 yards when hit with his 6-iron with a club head speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 12 times at the required speed.

Data from this test had a sample mean of 171.6 yards with a sample standard deviation of 2.4 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer’s requirements. Use the partial t-table below.

	Area in one tail
	0.025	0.05
	Area in two tails
Degrees of Freedom n - 1	0.05	0.10
6	2.447	1.943
7	2.365	1.895
8	2.306	1.860
9	2.262	1.833

A. Accept the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 170 yards.
B. Accept the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 170 yards.
C. Reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 170 yards.
D. Reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 170 yards.

Question 32 of 40

a 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 25.2. What is the margin of error?

A. 3.9

B. 4.8

C. 4.9

D. 3.7

Question 33 of 40

2.5 Points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.

	Colorblind	Not Colorblind	Total
Male	7	53	60
Female	1	39	40
Total	8	92	100

If gender and colorblindness are independent, find the expected values corresponding to the male combinations of gender and colorblindness.

A. Colorblind Male 4.8; Not Colorblind Male 55.2
B. Colorblind Male 6.8; Not Colorblind Male 53.2
C. Colorblind Male 4.8; Not Colorblind Male 55.4
D. Colorblind Male 4.8; Not Colorblind Male 56.2

Question 34 of 40

A 95% confidence interval for the mean of a normal population is found to be 17.6 < µ < 23.6. What is the margin of error?

A. 2.0

B. 2.7

C. 3.0

D. 4.0

Question 35 of 40

The critical value of χ2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the χ2 statistic in Problem 8 had been 3.427, state your conclusion about the relationship between gender and colorblindness.

A.Do not reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.

B.Do not reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.

C.Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.

D.Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.

Question 36 of 40

2.5 Points

A 95% confidence interval for the mean of a normal population is found to be 13.2 < µ < 22.4. What is the margin of error?

A. 4.6
B. 4.4
C. 4.2
D. 5.6
Question 37 of 40	2.5 Points

The following data were analyzed using one-way analysis of variance.

A	B	C
34	27	19
26	23	31
31	29	22
28	21	22

Which one of the following statements is correct?

A. The purpose of the analysis is to determine whether the groups A, B, and C are independent.
B. The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal.
C. The purpose of the analysis is to test the hypothesis that the population variances of the three groups are equal.
D. The purpose of the analysis is to test the hypothesis that the sample means of the three groups are equal.

Question 38 of 40

2.5 Points

A golfer wished to find a ball that would travel more than 170 yards when hit with his 6-iron with a club head speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 12 times at the required speed. State the null and alternative hypotheses for this test.

A.H0: µ > 170; Ha: µ = 170

B.H0: µ < 170; Ha: µ = 170

C.H0: µ = 170; Ha: µ > 170

D.H0: µ = 160; Ha: µ > 160

Question 39 of 40

2.5 Points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.

	Colorblind	Not Colorblind	Total
Male	7	53	60
Female	1	39	40
Total	8	92	100

State the null and alternative hypothesis for the information above.

A. H0: Colorblindness and gender are dependent characteristics. Ha: Colorblindness and gender are related in some way.
B. H0: Colorblindness and gender are independent characteristics. Ha: Colorblindness and gender are not related in any way.
C. H0: Colorblindness and gender are dependent characteristics. Ha: Colorblindness and gender are not related in any way.
D. H0: Colorblindness and gender are independent characteristics. Ha: Colorblindness and gender are related in some way.

Question 40 of 40

A large test statistic F tells us that the sample means __________ the data within the individual samples, which would be unlikely if the populations means really were equal (as the null hypothesis claims).

A. differ more than

B. differ less than

C. are equal to

D. do not vary with