Question

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.

Male   Female
27,927   20,148
14,850   24,892
6,324   5,396
28,793   19,140
26,459   10,862
6,331   16,212
21,862   10,044
17,046   19,135
26,084   13,129
21,814   20,366
11,281   16,227
10,646   12,021
12,117   17,875
22,161   22,720
20,445   4,559
777   19,113
19,858   22,515
9,697   17,186
21,106   16,356
16,351   12,606
17,379   29,934
21,860   9,533
9,490   15,950
8,727   7,057
25,605   11,467
10,938   17,266
13,660   14,053
12,902   20,586
12,420   21,947
19,386   13,760
12,208   34,815
8,785   6,963
20,279   11,051
18,780   11,383
10,942   29,385
14,293   20,829
16,338   16,538
9,692   18,877
17,919   19,691
12,542   16,350
13,288   20,009
4,492   12,051
18,659   17,262
12,905   15,835
16,066   29,738
17,528   37,631
17,176   26,754
39,110   35,995
17,427   26,199
45,872   33,488
26,231   18,078
9,468   7,326
16,372   25,366
10,868   16,571
7,911   13,590
19,102   28,627

a. Use a

0.050.05

significance level to test the claim that among​ couples, males speak fewer words in a day than females.In this​ example,

mu Subscript dμd

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?

Upper H 0H0​:

mu Subscript dμd

▼

less than<

greater than>

not equals≠

equals=

nothing ​word(s)

Upper H 1H1​:

mu Subscript dμd

▼

less than<

equals=

not equals≠

greater than>

nothing ​word(s)

​(Type integers or decimals. Do not​ round.)

Identify the test statistic.

tequals=nothing

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

Since the​ P-value is

▼

less than or equal to

greater than

the significance​ level,

▼

fail to reject

reject

the null hypothesis. There

▼

is not

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

nothing

​word(s)less than<mu Subscript dμdless than<nothing

​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

▼

only negative numbers,

only positive numbers,

zero,

▼

fail to reject

reject

the null hypothesis.

Enter your answer in each of the answer boxes.

Answer 1

Following table shows the calculations:

	Male	Female	d	(d-mean)^2
	27,927	20148	7779	92823590.25
	14,850	24892	-10042	67018782.25
	6,324	5396	928	7747872.25
	28,793	19140	9653	132445572.3
	26,459	10862	15597	304589756.3
	6,331	16212	-9881	64408650.25
	21,862	10044	11818	186964602.3
	17,046	19135	-2089	54522.25
	26,084	13129	12955	219350910.3
	21,814	20366	1448	10913112.25
	11,281	16227	-4946	9551190.25
	10,646	12021	-1375	230880.25
	12,117	17875	-5758	15229506.25
	22,161	22720	-559	1680912.25
	20,445	4559	15886	314760822.3
	777	19113	-18336	271606880.3
	19,858	22515	-2657	642402.25
	9,697	17186	-7489	31736322.25
	21,106	16356	4750	43632630.25
	16,351	12606	3745	31365600.25
	17,379	29934	-12555	114479300.3
	21,860	9533	12327	201143306.3
	9,490	15950	-6460	21201420.25
	8,727	7057	1670	12429150.25
	25,605	11467	14138	255792042.3
	10,938	17266	-6328	20003256.25
	13,660	14053	-393	2138906.25
	12,902	20586	-7684	33971412.25
	12,420	21947	-9527	58851912.25
	19,386	13760	5626	55972842.25
	12,208	34815	-22607	430624752.3
	8,785	6963	1822	13524006.25
	20,279	11051	9228	122843972.3
	18,780	11383	7397	85608756.25
	10,942	29385	-18443	275145156.3
	14,293	20829	-6536	21907080.25
	16,338	16538	-200	2740680.25
	9,692	18877	-9185	53721570.25
	17,919	19691	-1772	6972.25
	12,542	16350	-3808	3812256.25
	13,288	20009	-6721	23673090.25
	4,492	12051	-7559	32529912.25
	18,659	17262	1397	10578756.25
	12,905	15835	-2930	1154550.25
	16,066	29738	-13672	139629672.3
	17,528	37631	-20103	332971256.3
	17,176	26754	-9578	59637006.25
	39,110	35995	3115	24705870.25
	17,427	26199	-8772	47837972.25
	45,872	33488	12384	202763360.3
	26,231	18078	8153	100170072.3
	9,468	7326	2142	15980006.25
	16,372	25366	-8994	50958182.25
	10,868	16571	-5703	14803256.25
	7,911	13590	-5679	14619152.25
	19,102	28627	-9525	58821230.25
	Total		-103908	4723506614

--------------------------------------------------------------------------------------

(B)

First we need to find the 90% confidence interval. The 90% confidence interval is

The required confidence interval is ( -3927.324, infinity).

Since confidence interval contains zero so we fail to reject the null hypothesis on the basis of confidence interval.