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 25,697 21,057 15,805 25,188 6,754 6,720 29,295 19,478 24,493 10,387 7,690 17,490 22,966 10,592 16,234 20,441 25,234 15,266 21,404 18,779 10,569 16,002 11,003 13,263 14,379 15,743 22,470 22,604 20,639 4,463 331 17,409 21,684 22,882 8,949 18,644 20,869 15,700 15,430 13,346 15,092 29,768 20,863 8,058 7,547 18,749 5,206 6,165 27,657 12,683 8,948 19,135 11,555 14,109 12,097 20,970 14,231 19,520 20,093 11,976 13,899 33,421 7,806 7,179 18,987 10,440 16,050 9,999 9,002 29,678 14,964 22,133 15,349 16,398 11,290 18,091 18,394 20,238 13,695 16,087 11,941 17,346 5,378 12,657 19,146 15,660 15,359 17,944 16,472 27,787 14,910 40,139 18,261 25,610 37,646 36,712 15,786 24,828 45,455 32,824 26,859 18,416 8,709 8,765 16,230 24,404 8,512 17,480 7,659 15,972 21,032 28,191 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, μd 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: μd ________ ( A. =, B. ≠, C. <, D. > ) _______ words(s) H1: μd _______ ( 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) < μd < ___________ 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.
Section 9.3
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
|
|
|---|---|---|
|
25,697
|
21,057
|
|
|
15,805
|
25,188
|
|
|
6,754
|
6,720
|
|
|
29,295
|
19,478
|
|
|
24,493
|
10,387
|
|
|
7,690
|
17,490
|
|
|
22,966
|
10,592
|
|
|
16,234
|
20,441
|
|
|
25,234
|
15,266
|
|
|
21,404
|
18,779
|
|
|
10,569
|
16,002
|
|
|
11,003
|
13,263
|
|
|
14,379
|
15,743
|
|
|
22,470
|
22,604
|
|
|
20,639
|
4,463
|
|
|
331
|
17,409
|
|
|
21,684
|
22,882
|
|
|
8,949
|
18,644
|
|
|
20,869
|
15,700
|
|
|
15,430
|
13,346
|
|
|
15,092
|
29,768
|
|
|
20,863
|
8,058
|
|
|
7,547
|
18,749
|
|
|
5,206
|
6,165
|
|
|
27,657
|
12,683
|
|
|
8,948
|
19,135
|
|
|
11,555
|
14,109
|
|
|
12,097
|
20,970
|
|
|
14,231
|
19,520
|
|
|
20,093
|
11,976
|
|
|
13,899
|
33,421
|
|
|
7,806
|
7,179
|
|
|
18,987
|
10,440
|
|
|
16,050
|
9,999
|
|
|
9,002
|
29,678
|
|
|
14,964
|
22,133
|
|
|
15,349
|
16,398
|
|
|
11,290
|
18,091
|
|
|
18,394
|
20,238
|
|
|
13,695
|
16,087
|
|
|
11,941
|
17,346
|
|
|
5,378
|
12,657
|
|
|
19,146
|
15,660
|
|
|
15,359
|
17,944
|
|
|
16,472
|
27,787
|
|
|
14,910
|
40,139
|
|
|
18,261
|
25,610
|
|
|
37,646
|
36,712
|
|
|
15,786
|
24,828
|
|
|
45,455
|
32,824
|
|
|
26,859
|
18,416
|
|
|
8,709
|
8,765
|
|
|
16,230
|
24,404
|
|
|
8,512
|
17,480
|
|
|
7,659
|
15,972
|
|
|
21,032
|
28,191
|
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, μd 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: μd ________ ( A. =, B. ≠, C. <, D. > ) _______ words(s)
H1: μd _______ ( 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) < μd < ___________ 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.
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