Section 8.2

Question #8

A 9-year-old girl did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under her hand without seeing it and without touching it. Among 256 trials, the touch therapists were correct 114 times. Use a 0.10 significance level to test the claim that touch therapists use a method equivalent to random guesses. Do the results suggest that touch therapists are effective?

Identify the null and alternative hypotheses for this test. Choose the correct answer below.

A. H₀: p=0.5

H₁: p0.5

B. H₀: p=0.5

H₁: p<0.5

C. H₀: p0.5

H₁: p=0.5

D. H₀: p=0.5

H₁: p>0.5

Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is ________.

(Round to two decimal places as needed.)

Identify the P-value for this hypothesis test.

The P-value for this hypothesis test is _________.

(Round to three decimal places as needed.)

Identify the conclusion for this hypothesis test.

A. Failtoreject H₀. There isnot sufficient evidence to warrant rejection of the claim that touch therapists use a method equivalent to random guesses.

B. Failtoreject H₀. There is sufficient evidence to warrant rejection of the claim that touch therapists use a method equivalent to random guesses.

C. Reject H₀. There is sufficient evidence to warrant rejection of the claim that touch therapists use a method equivalent to random guesses.

D. Reject H₀. There isnot sufficient evidence to warrant rejection of the claim that touch therapists use a method equivalent to random guesses.

Do the results suggest that touch therapists are effective?

The results suggest that the touch therapists performed __________ (A. similarly to B. worse than C. better than ) random guesses, so they __________( A. do not appear, B. appear ) to be effective.

Question #9

In one study of smokers who tried to quit smoking with nicotine patch therapy, 39 were smoking one year after treatment and 31 were not smoking one year after the treatment. Use a 0.05 significance level to test the claim that among smokers who try to quit with nicotine patch therapy, the majority are smoking one year after the treatment. Do these results suggest that the nicotine patch therapy is not effective?

Identify the null and alternative hypotheses for this test. Choose the correct answer below.

A. H₀: p=0.5

H₁: p0.5

B. H₀: p=0.5

H₁: p<0.5

C. H₀: p>0.5

H₁: p=0.5

D. H₀: p=0.5

H₁: p>0.5

Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is ________.

(Round to two decimal places as needed.)

Identify the P-value for this hypothesis test.

The P-value for this hypothesis test is _________.

(Round to three decimal places as needed.)

Identify the conclusion for this hypothesis test.

A. Failtoreject H₀. There sufficient evidence to warrant support of the claim that the majority are smoking one year after the treatment.

B. Failtoreject H₀. There insufficient evidence to warrant support of the claim that the majority are smoking one year after the treatment.

C. Reject H₀. There insufficient evidence to warrant support of the claim that the majority are smoking one year after the treatment.

D. Reject H₀. There sufficient evidence to warrant support of the claim that the majority are smoking one year after the treatment.

Do these results suggest that the nicotine patch therapy is not effective?

Since there is __________ ( A. insufficient, B. sufficient ) evidence to support the claim that the majority are smoking one year after the treatment, there is____________ ( A. sufficient B. insufficient) evidence to suggest that the nicotine patch is not effective.

Question #10

In a recent court case it was found that during a period of 11 years 856 people were selected for grand jury duty and 35% of them were from the same ethnicity. Among the people eligible for grand jury duty, 79.8% were of this ethnicity. Use a 0.01 significance level to test the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.

Which of the following is the hypothesis test to be conducted?

A. H₀:p=0.798

H₁:p>0.798

B. H₀:p>0.798

H₁:p=0.798

C. H₀:p<0.798

H₁:p=0.798

D. H₀:p=0.798

H₁:p<0.798

E. H₀:p0.798

H₁:p=0.798

F. H₀:p=0.798

H₁:p0.798

What is the test statistic?

z= _________

(Round to two decimal places as needed.)

What is the P-value?

P-value= __________

(Round to four decimal places as needed.)

What is the conclusion on the null hypothesis?

A. Reject the null hypothesis because the P-value is lessthanorequalto the significance level, .

B. Failtoreject the null hypothesis because the P-value is greaterthan the significance level, .

C. Reject the null hypothesis because the P-value is greaterthan the significance level, .

D. Failtoreject the null hypothesis because the P-value is lessthanorequalto the significance level, .

Does the jury selection system appear to be fair?

A. There isnot sufficient evidence to support the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. The jury selection process appears to be unfair.

B. There isnot sufficient evidence to warrant rejection of the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. The jury selection process appears to be fair.

C. There is sufficient evidence to warrant rejection of the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. The jury selection process appears to be fair.

D. There is sufficient evidence to support the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. The jury selection process appears to be unfair.

Section 8.3

Question #1

Twenty-four different video games showing druguse were observed. The duration times of druguse (in seconds) were recorded. When using this sample for a t test of the claim that the population mean is greater than 82 sec, what does df denote, and what is its value?

What does df denote?

A. The number of degrees of freedom

B. The sample size

C. The sample standard deviation

D. The test statistic

The value of df is ________.

(Type an integer or a decimal. Do not round.)

Question #2

Use technology to find the P-value for the hypothesis test described below.

The claim is that for a smartphone carrier's data speeds at airports, the mean is

=11.00 Mbps. The sample size is n=21 and the test statistic is t= 1.335.

P-value= __________ (Round to three decimal places as needed.)

Question #3

Use technology to find the P-value for the hypothesis test described below.

The claim is that for 12 AM body temperatures, the mean is <98.6F.

The sample size is n=9 and the test statistic is t=2.279.

P-value= __________ (Round to three decimal places as needed.)

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.