Section 9.3

Question #6

Data on the numbers of hospital admissions resulting from motor vehicle crashes are given below for Fridays on the 6th of a month and Fridays on the following 13th of the same month. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate of the mean of the population of differences between hospital admissions. Use the confidence interval to test the claim that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are not affected.

Friday the 6th	4	2	9	7	9
Fridaythe13th	11	13	11	12	12

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 number of hospital admissions on Friday the 6th minus the number of hospital admissions on Friday the 13th. Find the 95% confidence interval.

______________ < _d < ____________

(Round to two decimal places as needed.)

Based on the confidence interval, can one reject the claim that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are not affected?

A. Yes, because the confidence interval doesnotinclude zero.

B. No, because the confidence interval doesnotinclude zero.

C. No, because the confidence interval includes zero.

D. Yes, because the confidence interval includes zero.

Question #7

The data below are yields for two different types of corn seed that were used on adjacent plots of land. Assume that the data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate of the difference between type 1 and type 2 yields. What does the confidence interval suggest about farmer Joe's claim that type 1 seed is better than type 2 seed?

Type 1	2210	1994	2146	2465	2195	1934	2192	1467
Type 2	2092	1918	2049	2432	2173	1927	2122	1427

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 type 1 seed yield minus the type 2 seed yield.

The 95% confidence interval is ___________< _d < ___________.

(Round to two decimal places as needed.)

What does the confidence interval suggest about farmer Joe's claim that type 1 seed is better than type 2 seed?

A. Because the confidence interval includes zero, there is sufficient evidence to support farmer Joe's claim.

B. Because the confidence interval onlyincludespositivevaluesanddoesnotinclude zero, there is sufficient evidence to support farmer Joe's claim.

C. Because the confidence interval onlyincludespositivevaluesanddoesnotinclude zero, there isnot sufficient evidence to support farmer Joe's claim.

D. Because the confidence interval includes zero, there isnot sufficient evidence to support farmer Joe's claim.

Question #8

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	7.3	2.0	9.6	8.8	13.1	9.2	6.9	3.1
After	6.7	2.2	7.4	8.7	8.3	6.5	3.6	2.6

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 includeszero.

B. Yes, because the confidence interval doesnotincludezeroandisentirelygreater thanzero.

C. No, because the confidence interval doesnotincludezeroandisentirelygreater thanzero.

D. Yes, because the confidence interval

includeszero.

Question #9

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
29,035	20,661
16,851	22,830
6,592	4,190
29,752	18,209
25,531	11,122
7,470	17,459
21,988	12,639
16,339	17,896
26,824	14,763
21,994	19,521
10,766	14,803
12,000	12,907
10,924	18,878
21,671	22,615
20,057	6,798
2,132	18,044
21,804	23,041
10,807	18,339
20,332	14,664
16,459	12,532
17,590	31,866
22,609	8,289
7,468	18,062
6,928	6,694
24,975	11,253
11,161	18,240
11,883	12,876
13,114	23,159
14,394	21,072
17,204	13,005
13,661	33,315
9,832	9,245
21,342	8,891
19,078	11,247
11,232	28,982
15,751	19,294
16,199	15,452
11,873	17,374
19,586	20,212
12,616	16,432
15,528	18,478
6,216	11,692
19,824	18,636
15,117	18,087
17,426	30,678
17,427	38,310
21,003	25,822
39,319	35,030
16,069	23,606
45,132	32,831
24,482	19,162
9,184	8,121
17,211	26,446
10,684	15,069
5,269	14,992
19,670	27,588

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. > ) _______ words(s)

H₁: _d _______ ( A. =, B. , C. <, D. > ) ________ words(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. zero, B. only positive numbers, C. only negative numbers ) ____________ ( A. fail to reject, B. reject ) the null hypothesis.

Question #10

Refer to the data set in the accompanying table. Assume that the paired sample data is a simple random sample and the differences have a distribution that is approximately normal. Use a significance level of 0.05 to test for a difference between the weights of discarded paper (in pounds) and weights of discarded plastic (in pounds).

View the data.

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Household	Paper	Plastic
1		6.38		8.82
2		11.08		12.47
3		8.82		11.89
4		16.39		9.70
5		9.83		6.26
6		20.12		18.35
7		11.36		10.25
8		9.55		9.20
9		13.31		19.70
10		6.33		3.86
11		8.72		9.20
12		9.19		3.74
13		11.42		12.81
14		6.98		2.65
15		6.05		2.73
16		2.41		1.13
17		6.83		3.57
18		13.61		8.95
19		3.27		0.63
20		16.08		14.36
21		7.72		3.86
22		15.09		9.11
23		12.32		11.17
24		7.98		6.09
25		6.44		8.40
26		9.41		3.36
27		6.67		6.09
28		6.96		7.60
29		2.80		5.92
30		14.33		6.43
Household	Paper	Plastic

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 weight of discarded paper minus the weight of discarded plastic for a household. 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 that there is a difference between the weights of discarded paper and discarded plastic.