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Question : How many tissues should a package of tissues contain Researchers have determined : 2150537

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

36) How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 45 tissues during a cold. Suppose a random sample of 2500 people yielded the following data on the number of tissues used during a cold: overbar(x) = 33, s = 17. Using the sample information provided, set up the calculation for the test statistic for the relevant hypothesis test, but do not simplify.

A) z = (33 - 45/17)

B) z = (33 - 45/(17/2500^{2}))

C) z = (33 - 45/(17^{2}/2500))

D) z = (33 - 45/(17/√(2500)))

37) How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 53 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on the number of tissues used during a cold: overbar(x) = 48, s = 18. We want to test the alternative hypothesis H_{a}: μ < 53. State the correct rejection region for α = .05.

A) Reject H_{0} if z < -1.96.

B) Reject H_{0} if z > 1.645.

C) Reject H_{0} if z > 1.96 or z < -1.96.

D) Reject H_{0} if z < -1.645.

39) Consider the following printout.

HYPOTHESIS: VARIANCE X = x

X=gpa

SAMPLE MEAN OF X=2.8506

SAMPLE VARIANCE OF X=.18000

SAMPLE SIZE OF X=223

HYPOTHESIZED VALUE (x)=3.0

VARIANCE X - x=-.1494

z=-5.25856

Suppose we tested H_{a}: μ < 3.0. Find the appropriate rejection region if we used α = .05.

A) Reject if z > 1.645 or z < -1.645.

B) Reject if z > 1.96 or z < -1.96.

C) Reject if z < -1.96.

D) Reject if z < -1.645.

For the given value of α and observed significance level (p-value), indicate whether the null hypothesis would be rejected.

42) α = 0.01, p-value = 0.005

A) Reject H_{0}

B) Fail to reject H_{0}

43) α = 0.01, p-value = 0.09

A) Fail to reject H_{0}

B) Reject H_{0}

Solve the problem.

44) Consider a test of H_{0}: μ = 50 performed with the computer. SPSS reports a two-tailed p-value of 0.0574. Make the appropriate conclusion for the given situation: H_{a}: μ < 50, z = -1.9, α = 0.05

A) Reject H_{0}

B) Fail to reject H_{0}

45) Consider a test of H_{0}: μ = 45 performed with the computer. SPSS reports a two-tailed p-value of 0.0164. Make the appropriate conclusion for the given situation: H_{a}: μ > 45, z = -2.4, α = 0.01

A) Fail to reject H_{0}

B) Reject H_{0}

46) Consider a test of H_{0}: μ = 80 performed with the computer. SPSS reports a two-tailed p-value of 0.2112. Make the appropriate conclusion for the given situation: H_{a}: μ > 80, z = 1.25, α = 0.10

A) Reject H_{0}

B) Fail to reject H_{0}

47) Consider a test of H_{0}: μ = 80 performed with the computer. SPSS reports a two-tailed p-value of 0.0038. Make the appropriate conclusion for the given situation: H_{a}: μ ≠ 80, z = 2.9, α = 0.01

A) Reject H_{0}

B) Fail to reject H_{0}

48) Given H_{0}: μ = 25, H_{a}: μ ≠ 25, and p = 0.028. Do you reject or fail to reject H_{0} at the .01 level of significance?

A) reject H_{0}

B) fail to reject H_{0}

C) not sufficient information to decide

49) Given H_{0}: μ = 18, H_{a}: μ < 18, and p = 0.081. Do you reject or fail to reject H_{0} at the .05 level of significance?

A) fail to reject H_{0}

B) reject H_{0}

C) not sufficient information to decide

50) A bottling company produces bottles that hold 10 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 49 bottles and finds the average amount of liquid held by the bottles is 9.9155 ounces with a standard deviation of 0.35 ounce. Suppose the p-value of this test is 0.0455. State the proper conclusion.

A) At α = 0.025, reject the null hypothesis.

B) At α = 0.10, fail to reject the null hypothesis.

C) At α = 0.05, accept the null hypothesis.

D) At α = 0.05, reject the null hypothesis.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

54) Consider the following printout.

HYPOTHESIS: MEAN X = x

X =gpa

SAMPLE MEAN OF X =2.9528

SAMPLE VARIANCE OF X =0.226933

SAMPLE SIZE OF X =167

HYPOTHESIZED VALUE (x) = 3

MEAN X - x =-0.0472

z =-1.2804

Suppose a two-tailed test is desired. Find the p-value for the test.

A) p = 0.2006

B) p = 0.1003

C) p = 0.7994

D) p = 0.8997

55) A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 15 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. To determine whether the site meets the organization's requirements, consider the test, H_{0}: μ = 15 vs. H_{a}: μ > 15, where μ is the true mean wind speed at the site and α = .10. Suppose the observed significance level (p-value) of the test is calculated to be p = 0.2728. Interpret this result.

A) Since the p-value greatly exceeds α = .10, there is strong evidence to reject the null hypothesis.

B) We are 72.72% confident that μ = 15.

C) The probability of rejecting the null hypothesis is 0.2728.

D) Since the p-value exceeds α = .10, there is insufficient evidence to reject the null hypothesis.

Answer the question True or False.

59) The smaller the p-value in a test of hypothesis, the more significant the results are.

A) True

B) False

61) In a test of H0: μ = 70 against Ha: μ ≠70, the sample data yielded the test statistic z = 2.11. Find and interpret the p-value for the test.

62) In a test of H0: μ = 12 against Ha: μ > 12, a sample of n = 75 observations possessed mean overbar(x) = 13.1 and standard deviation s = 4.3. Find and interpret the p-value for the test.

63) In a test of H0: μ = 250 against Ha: μ ≠ 250, a sample of n = 100 observations possessed mean overbar(x) = 247.3 and standard deviation s = 11.4. Find and interpret the p-value for the test.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

66) How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 54 tissues during a cold. Suppose a random sample of 100 people yielded the following data on the number of tissues used during a cold: overbar(x) = 46, s = 20. Suppose the corresponding test statistic falls in the rejection region at α = .05. What is the correct conclusion?

A) At α = .05, accept H_{a}.

B) At α = .05, reject H_{0}.

C) At α = .10, reject H_{0}.

D) At α = .10, reject H_{a}.

67) We have created a 90% confidence interval for μ with the result (8, 13). What conclusion will we make if we test H_{0}: μ = 17 vs. H_{a}: μ ≠ 17 at α = .10?

A) Reject H_{0} in favor of H_{a}.

B) Fail to reject H_{0}.

C) Accept H_{0} rather than H_{a}.

D) We cannot tell what our decision will be with the information given.

68) Suppose we wish to test H_{0}: μ = 34 vs. H_{a}: μ < 34. Which of the following possible sample results gives the most evidence to support H_{a} (i.e., reject H_{0})?

A) overbar(x) = 31, s = 7

B) overbar(x) = 30, s = 4

C) overbar(x) = 30, s = 9

D) overbar(x) = 32, s = 5

69) Consider the following printout.

HYPOTHESIS: VARIANCE X = x

X=gpa

SAMPLE MEAN OF X=2.5824

SAMPLE VARIANCE OF X=.25000

SAMPLE SIZE OF X=192

HYPOTHESIZED VALUE (x)=2.7

VARIANCE X - x=-.1176

z=-3.25903

State the proper conclusion when testing H_{0}: μ = 2.7 vs. H_{a}: μ < 2.7 at α = .05.

A) Reject H_{0}.

B) Accept H_{0}.

C) Fail to reject H_{0}.

D) We cannot determine from the information given.

70) Consider the following printout.

HYPOTHESIS: VARIANCE X = x

X=gpa

SAMPLE MEAN OF X=3.2969

SAMPLE VARIANCE OF X=.24000

SAMPLE SIZE OF X=200

HYPOTHESIZED VALUE (x)=3.4

VARIANCE X - x=-.1031

z=-2.97624

Is this a large enough sample for this analysis to work?

A) Yes, since the np > 15 and nq > 15.

B) No.

C) Yes, since the population of GPA scores is approximately normally distributed.

D) Yes, since n = 200, which is greater than 30.

71) A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 20 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. Based on a sample of n = 32 wind speed recordings (taken at random intervals), the wind speed at the site averaged overbar(x) = 20.8 mph, with a standard deviation of s = 4.1 mph. To determine whether the site meets the organization's requirements, consider the test, H_{0}: μ = 20 vs. H_{a}: μ > 20, where μ is the true mean wind speed at the site and α = .01. Suppose the value of the test statistic were computed to be 1.10. State the conclusion.

A) We are 99% confident that the site does not meet the organization's requirements.

B) We are 99% confident that the site meets the organization's requirements.

C) At α = .01, there is insufficient evidence to conclude the true mean wind speed at the site exceeds 20 mph.

D) At α = .01, there is sufficient evidence to conclude the true mean wind speed at the site exceeds 20 mph.