stats homework help

stats_8.docx

Home >Mathematics homework help >stats homework help

1. 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. Ho: µ = 9.3 minutes H  : µ < 9.3 minutes
B. Ho: µ = 9.3 minutes H  : µ > 9.3 minutes
C. Ho: µ = 9.3 minutes H  : µ  9.3 minutes
D. Ho: µ  9.3 minutes H  : µ = 9.3 minutes

2. 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

3. 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.

4. 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

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.

Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported.

Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported.

Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported.

Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported.

6. 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

7. 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

8. 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%

9. 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.

10. 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

11. 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.

12. 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

13. 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.

14. 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

15. 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.

16. 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.

17. 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

18. 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

19. 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.

20.

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

21. 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

22. 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

State the null and alternative hypothesis for the test associated with this data.

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

23. 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 #21 had been 4.613, state your conclusion about the relationship between gender and colorblindness.

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

24. 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.

25. 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.

26. 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

27. The critical value of χ 2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the χ 2 statistic in Problem 8 had been 3.179, state your conclusion about the relationship between gender and colorblindness.

A. Do not reject H0.
B. Reject H0.
C. There is sufficient evidence to support the claim that gender and colorblindness are not related.
D. There is not sufficient evidence to accept or reject H0.

28. 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.

29. 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.

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.

30. 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 female combinations of gender and colorblindness.

A. Colorblind Female 4.8; Not Colorblind Female 55.2
B. Colorblind Female 3.2; Not Colorblind Female 36.8
C. Colorblind Female 4.8; Not Colorblind Female 35.2
D. Colorblind Female 3.8; Not Colorblind Female 36.2

31. 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.

32. 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

33. Which of the following statements is true?

A. The t distribution can be used when finding a confidence interval for the population mean whenever the sample size is small.
B. The p distribution can be used when finding a confidence interval for the population mean whenever the sample size is small.
C. The t distribution cannot be used when finding a confidence interval for the population mean whenever the sample size is small.
D. The p distribution cannot be used when finding a confidence interval for the sample mean whenever the sample size is small.

34. 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. State the null and alternative hypotheses for this test.

A. H0: µ = 180; Ha: µ > 180
B. H0: µ > 180; Ha: µ > 180
C. H0: µ < 180; Ha: µ > 180
D. H0: µ = 180; Ha: µ < 180

35. 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

36. 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.

37. 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.

38. The __________ test statistic is for the one-way analysis of variance.

A. P-Value
B. t
C. F
D. p

39. 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.

40. 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