Question

The accompanying table lists the numbers of words spoken in a day by each member of 56 different randomly sellected couples. Complete parts (a) and (b) below Click the icon to viaw the data on words spoken in a day by the couples . Use a 0.05 significance level to test the claim that among couples, males speak fewer words in a day than females. n this example, u is the mean value of the differences d for the population of all pairs of data, where each individual diference d is defined as the words spoken by the male minus words spoken the female, What are the nul and alternative hypotheses for the hypothesis test? Ho H word(s) wnrdie) (Type intagars or decimals Do not round ) Identify e tast statistic Round to two decimal placas as needod) Identify the Pvalue. (Round to three decimal places as needed.) Pvalue What is the conclusion based on the hypothesis test? Since the Pyalue is daim that malos speak fewer words in a day than females. the nul hypathesis There sufficient evidence to support e significance level . Construct the confidence interval that could be used for the hypothesis test dascribed in part (a) What featura of the canfidence intarval leads to the same conckusion reached in part (a)? The confidanca intarval isward(s)<award(s) (Round to one decimal place as needed.) What feature of the confidence interval leads to the same conclusion reached in part (a)? the null hypothesis. Since the confidence interval conteins

Male   Female
26,074   19,013
16,287   23,407
4,653   6,741
27,303   20,492
27,421   12,617
9,766   16,363
20,440   9,681
16,037   20,662
25,807   15,383
21,658   20,273
13,174   14,025
8,961   11,426
11,048   17,812
22,170   25,246
20,157   6,670
1,253   20,301
22,236   22,622
8,189   19,656
21,245   15,824
18,515   13,500
16,672   28,908
20,342   8,624
6,949   19,482
5,296   5,253
26,184   11,851
10,025   19,892
13,862   15,628
12,540   23,166
13,604   21,991
20,680   12,842
13,560   34,635
10,884   8,683
21,390   9,058
16,973   11,517
12,169   30,822
14,841   21,245
13,989   17,289
8,789   19,478
18,887   22,051
12,016   17,502
12,824   17,436
4,104   13,099
19,842   18,497
14,371   16,612
17,898   29,305
14,905   36,938
20,136   23,761
38,449   35,048
15,525   22,515
45,070   32,343
26,663   18,086
10,334   7,556
15,844   23,283
11,092   16,780
5,445   13,631
21,394   28,207

Answer 1

a) From the given data

Male	Female	Difference
26074	19013	7061
16287	23407	-7120
4653	6741	-2088
27303	20492	6811
27421	12617	14804
9766	16363	-6597
20440	9681	10759
16037	20662	-4625
25807	15383	10424
21658	20273	1385
13174	14025	-851
8961	11426	-2465
11048	17812	-6764
22170	25246	-3076
20157	6670	13487
1253	20301	-19048
22236	22622	-386
8189	19656	-11467
21245	15824	5421
18515	13500	5015
16672	28908	-12236
20342	8624	11718
6949	19482	-12533
5296	5253	43
26184	11851	14333
10025	19892	-9867
13862	15628	-1766
12540	23166	-10626
13604	21991	-8387
20680	12842	7838
13560	34635	-21075
10884	8683	2201
21390	9058	12332
16973	11517	5456
12169	30822	-18653
14841	21245	-6404
13989	17289	-3300
8789	19478	-10689
18887	22051	-3164
12016	17502	-5486
12824	17436	-4612
4104	13099	-8995
19842	18497	1345
14371	16612	-2241
17898	29305	-11407
14905	36938	-22033
20136	23761	-3625
38449	35048	3401
15525	22515	-6990
45070	32343	12727
26663	18086	8577
10334	7556	2778
15844	23283	-7439
11092	16780	-5688
5445	13631	-8186
21394	28207	-6813

Descriptive Statistics: Difference Total Variance Sum of Squares Variable Count Mean StDev Sum Difference 56 -2121.179 9170.049 84089801 -118786 4876905356

1. Null and Alternative Hypothesis:

H0: Males speak do not fewer words in a day than females
H1: Males speak fewer words in a day than females

i.e.

Ho: 0 Ha: u 0 This corresponds to a left-tailed test, for which a t-test for two paired samples be used. (2) Rejection Region Based on the information provided, the significance level is a 0.05, and the degrees of freedom are df 55 Hence, it is found that the critical value for this left-tailed test is te = -1.673, for a = 0.05 and df = 55 The rejection region for this left-tailed test is R -1.673} {t:t (3) Test Statistics The t-statistic is computed as shown in the following formula: D 2121.179 -1.731 t sp 9170.049/56 (4) Decision about the null hypothesis 1.673, it is then concluded that the null hypothesis is Since it is observed that t -1.731 <te rejected Using the P-value approach: The p-value is p 0.0445, and since p 0.0445 0.05, it is concluded that the null hypothesis is rejected (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean is less than 2, at the 0.05 significance level.

Answers: t = -1.731

P-value = 0.0445

since P-value = 0.0445 less than significance level alpha 0.05, we reject the null hypothesis.

There is sufficient evidence to support that claim that males speak fewer words in a day than females.

b)

The 95% confdence difference between population means =-2121.179t1.6730349170.049 = (-4171.311,-71.04584) 56 S d ttsy-1-8 af

since the confidence interval contains not zero therefore reject the null hypothesis