Question

Question Help Listed below are the numbers of words spoken in a day by each member of eight different randomly selected couples. Complete parts (a) and (b) below. Horo на на Male 15,983 26.708 1376 7767 18,154 15.226 13,817 26,688 Female 25,135 13,052 17,803 18,096 12,701 17,478 15,776 18,807 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, He 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? word(s) word(s) (Type integers or decimals. Do not round.) Identity the test statistic 1=(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 the significance level the null hypothesis. There sufficient evidence to support the claim that males speak tewer 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 Enter your answer in each of the answer boxes. hulu hulu

Answer 1

a) Null and Alternative Hypothesis:

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From the given data

S.NO.	Male (X)	Female (Y)	di = Xi - Yi	d^2
1	15983	25135	-9152	83759104
2	26708	13052	13656	186486336
3	1376	17803	-16427	269846329
4	7767	18096	-10329	106688241
5	18154	12701	5453	29735209
6	15226	17478	-2252	5071504
7	13817	15776	-1959	3837681
8	26688	18807	7881	62110161
	Total :	-13129	747534565

d='Σά Ξ -13129 =-1641.125 8 η ο 1 1 S. Σα – nd [747534565-8*(-1641.125)?] =10183.93585 1 - Ε 8 -1 Test statistic d -1641.125 s/m 10183.93858 / 8 =-0.46

P-Value: 0.3312

Since the p-vlaue is greater than the significance level, so we accept the null hypothesis. There is not sufficient evidence to support the claim that the males speak fewer words in a day than females

b) Confidence interval:

The 95% confidence difference between population means 10183.93585 = -1641.125+ 2.3646 = (-10155.12 , 6872.86 18 S S aztan-lds Jn dtg%8–1=7df n

The interval contain Zero, so we accept the null hypothesis.

Thus we conclude that the males speak not fewer words in a day than females