Section 8.3

Question #7

In a test of the effectiveness of garlic for lowering cholesterol, 81 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg/dL) have a mean of

0.4 and a standard deviation of 1.86. Use a 0.01 significance level to test the claim that with garlic treatment, the mean change in LDL cholesterol is greater than 0. What do the results suggest about the effectiveness of the garlic treatment? Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

What are the null and alternative hypotheses?

A. H₀: =0 mg/dL

H₁: >0 mg/dL

B. H₀: =0 mg/dL

H₁: 0 mg/dL

C. H₀: >0 mg/dL

H₁: <0 mg/dL

D. H₀: =0 mg/dL

H₁: <0 mg/dL

Determine the test statistic.

___________ (Round to two decimal places as needed.)

Determine the P-value.

__________ (Round to three decimal places as needed.)

State the final conclusion that addresses the original claim.

__________ (A. Reject, B. Fail to reject) H₀. There is ___________ (A. not sufficient, B. sufficient) evidence to conclude that the mean of the population of changes __________ (A. is less than, B. is greater than, C. is not, D. equal to ) 0.

Question #8

A data set lists earthquake depths. The summary statistics are n=600, x=5.34 km, s=4.17

km. Use a 0.01 significance level to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 5.00. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

What are the null and alternative hypotheses?

A. H₀: =5.00 km

H₁: >5.00 km

B. H₀: =5.00 km

H₁: 5.00 km

C. H₀: 5.00 km

H₁: =5.00 km

D. H₀: =5.00 km

H₁: <5.00 km

Determine the test statistic.

_________(Round to two decimal places as needed.)

Determine the P-value.

___________ (Round to three decimal places as needed.)

State the final conclusion that addresses the original claim.

____________ (A. Fail to reject, B. reject ) H₀. There is ______________( A. sufficient, B. not sufficient ) evidence to conclude that the mean of the population of earthquake depths is 5.00 km __________ (A. is, B. is not) correct.

Question #9

Listed below are the lead concentrations in g/g measured in different traditional medicines. Use a 0.05 significance level to test the claim that the mean lead concentration for all such medicines is less than 22 g/g. Assume that the sample is a simple random sample.

19.58 21.51913 16.5 22.522.5 14.513

Assuming all conditions for conducting a hypothesis test are met, what are the null and alternative hypotheses?

A. H₀: =22 g/g

H₁: <22 g/g

B. H₀: >22 g/g

H₁: <22 g/g

C. H₀: =22 g/g

H₁: >22 g/g

D. H₀: =22 g/g

H₁: 22 g/g

Determine the test statistic.

_________ (Round to two decimal places as needed.)

Determine the P-value.

__________ (Round to three decimal places as needed.)

State the final conclusion that addresses the original claim.

__________ (A. Fail to reject, B. reject) H₀. There is _________ (A. sufficient, B. not sufficient) evidence to conclude that the mean lead concentration for all such medicines is __________ (A. not, B. equal to , C. less than, D. greater than ) 16 g/g.

Question #10

A group of students estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a 0.10 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute?

70

80

37

68

41

21

59

66

66

47

66

72

93

88

66

Assuming all conditions for conducting a hypothesis test are met, what are the null and alternative hypotheses?

A. H₀: =60 seconds

H₁: 60 seconds

B. H₀: 60 seconds

H₁: =60 seconds

C. H₀: =60 seconds

H₁: >60 seconds

D. H₀: =60 seconds

H₁: <60 seconds

State the final conclusion that addresses the original claim.

__________( A. Fail to reject, B. reject) H₀. There is _________ (A. sufficient, B. not sufficient) evidence to conclude that the mean of the population of estimates is 60 seconds ___________ ( A. is not, B. is) correct. It __________ (A. appears, B. does not appear) that, as a group, the students are reasonably good at estimating one minute.

Question #11

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.01 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement?

6696351257574583518

What are the hypotheses?

A. H₀: =1000 hic

H₁: <1000 hic

B. H₀: =1000 hic

H₁: 1000 hic

C. H₀: <1000 hic

H₁: 1000 hic

D. H₀: >1000 hic

H₁: <1000 hic

Identify the test statistic.

t= __________

(Round to three decimal places as needed.)

Identify the P-value.

The P-value is _______________

(Round to four decimal places as needed.)

State the final conclusion that addresses the original claim.

__________( A. Fail to reject, B. reject) H₀. There is _________ (A. sufficient, B. not sufficient)

evidence to support the claim that the sample is from a population with a mean less than 1000 hic.

What do the results suggest about the child booster seats meeting the specified requirement?

A. There is strong evidence that the mean is less than 1000 hic, but one of the booster seats has a measurement that is greater than 1000 hic.

B. There isnot strong evidence that the mean is less than 1000 hic, and one of the booster seats has a measurement that is greater than 1000 hic.

C. The results are inconclusive regarding whether one of the booster seats could have a measurement that is greater than 1000 hic.

D. The requirement is met since most sample measurements are less than 1000 hic.