Question #7

A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain scale before and after hypnosis. Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval for the mean of the

"beforeafter" differences. Does hypnotism appear to be effective in reducing pain?

Before	8.6	4.1	10.9	10.2	6.9	9.7	3.1	0.8
After	6.5	2.6	7.7	8.1	8.8	6.4	3.9	2.2

Construct a 95% confidence interval for the mean of the "beforeafter" differences.

___________ < _d < __________ (Round to two decimal places as needed.)

Does hypnotism appear to be effective in reducing pain?

A. No, because the confidence interval

doesnotincludeandisentirelygreaterthan

zero.

B. No, because the confidence interval includeszero.

C. Yes, because the confidence interval

doesnotincludeandisentirelygreaterthan

zero.

D. Yes, because the confidence interval includeszero.

Question #8

Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Use a

0.10 significance level to test for a difference between the measurements from the two arms. What can be concluded?

Right arm	151	138	117	129	134
Left arm	169	165	180	147	135

In this example, _d is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the measurement from the right arm minus the measurement from the left arm. What are the null and alternative hypotheses for the hypothesis test?

A. H₀: _d 0

H₁: _d = 0

B. H₀: _d = 0

H₁: _d < 0

C. H₀: _d = 0

H₁: _d 0

D. H₀: _d 0

H₁: ₁ > 0

Identify the test statistic.

t= ____________ (Round to two decimal places as needed.)

Identify the P-value.

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

What is the conclusion based on the hypothesis test?

Since the P-value is ____________( A. less, B. greater ) the significance level, __________( A. Fail to reject, B. Reject )the null hypothesis. There ___________ ( A. is not, B. is ) sufficient evidence to support the claim of a difference in measurements between the two arms.

Question #10

The accompanying table lists the numbers of words spoken in a day by each member of

56 different randomly selected couples. Complete parts (a) and (b) below.

View the data on words spoken in a day by the couples.

Words spoken in a day

Male	Female
26,426	19,099
15,563	22,949
7,364	6,220
26,851	18,152
24,680	11,427
9,663	13,806
20,956	11,533
18,166	18,690
25,559	15,134
20,316	19,620
12,013	14,785
12,166	11,739
14,486	16,647
21,112	24,775
20,587	6,589
159	17,487
18,509	22,021
9,186	19,726
21,274	17,873
16,276	14,266
14,258	30,485
21,256	8,257
7,627	18,885
8,537	4,310
25,698	11,497
10,709	17,305
15,056	14,838
10,771	20,728
15,271	20,130
20,409	13,532
14,839	33,608
10,054	9,152
18,856	12,431
16,891	11,932
11,786	30,003
13,440	21,046
16,253	17,842
9,461	19,254
20,520	20,346
9,773	14,730
15,080	17,295
6,461	12,829
17,319	16,484
12,279	18,181
17,189	28,191
15,109	36,985
18,397	24,776
35,791	33,106
18,601	24,908
47,626	32,155
27,587	20,457
8,467	6,526
16,840	23,904
10,068	16,155
7,847	13,012
19,005	28,507

a. Use a 0.05 significance level to test the claim that among couples, males speak fewer words in a day than females.

In this example, _d is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the words spoken by the male minus words spoken by the female. What are the null and alternative hypotheses for the hypothesis test?

H₀: _d ________ ( A. , B. >, C. <, D. = ) _____________word(s)

H₁: _d _________ ( A. , B. >, C. <, D. = ) _____________word(s)

(Type integers or decimals. Do not round.)

Identify the test statistic.

t= __________ (Round to two decimal places as needed.)

Identify the P-value.

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

What is the conclusion based on the hypothesis test?

Since the P-value is ____________( A. less than or equal to, B. greater than ) the significance level, __________( A. Fail to reject, B. Reject )the null hypothesis. There ___________ ( A. is not, B. is ) sufficient evidence to support the claim that males speak fewer words in a day than females.

b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)?

The confidence interval is ___________word(s) < _d < ___________ word(s).

(Round to one decimal place as needed.)

What feature of the confidence interval leads to the same conclusion reached in part (a)?

Since the confidence interval contains ____________ ( A. only positive numbers, B. zero, C. only negative numbers ) _____________ ( A. reject, B. fail to reject ) the null hypothesis.