Question

^{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. Male 15,872 25,816 1461 7988 18,247 15,214 14,017 24,920 2 Female 24,620 13,031 18,262 17,336 13,250 16,651 16,269 17,969 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.) Ho Hal Ha Ha}

^{Find the T}

^{Find the P-value}

^{ANd confidence intervals}

Answer 1

t-Test: Paired Two Sample for Means male 15872 25816 1461 7988 18247 15214 14017 24920 female 24620 13031 18262 17336 13250 16651 16269 17969 Mean Variance Observations Pearson Correlation Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail male female 15441.9 17173.5 6.6E+07 1.3E+07 8 8 -0.28528 0 7 -0.50209 0.3155 1.89458 0.63101 2.36462

RGui (64-bit) - [R Console) File Edit View Misc Packages Windows Help Oo STOP > male [1] 15872 25816 1461 7988 18247 15214 14017 24920 > female [1] 24620 13031 18262 17336 13250 16651 16269 17969 > > t.test (male, female, paired=T) Paired t-test data: male and female t = -0.50209, df = 7, p-value = 0.631 alternative hypothesis: true difference in means is not equal to o 95 percent confidence interval: -9886.745 6423.495 sample estimates: mean of the differences -1731.625

Excel & R software output for paired t test is attached above.

### Answers:

a] H0: μd = 0

H1: μd < 0

b]test statistics is t = -0.502 (negative sign)

df =7

c] p-value = 0.316

d] 95% confidence interval for mean difference is ( -9886.745 , 6423.495 )