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 15,536 25,576 1419 7737 18,362 15,734 13,680 25,846 Female 24,586 12,994 17,654 17,249 12,975 17,143 16,256 18,690 a. Use a 0.01 significance level to test the claim that among​ couples, males speak fewer words in a day than females. b. find the t statistic c. find the p value?

Answer 1

For Male :   

Sample mean using excel function AVERAGE(), x̅1 = 15486.25

Sample standard deviation using excel function STDEV.S, s1 = 8269.239087

Sample size, n1 = 8   

For Female :   

Sample mean using excel function AVERAGE(), x̅2 = 17193.375

Sample standard deviation using excel function STDEV.S, s2 = 3653.114285

Sample size, n2 = 8

Null and Alternative hypothesis:  

Ho : µ1 ≥ µ2  

H1 : µ1 < µ2  

Test statistic:  

t = (x̅1 - x̅2)/√(s1²/n1 + s2²/n2) = (15486.25 - 17193.375)/√(8269.2391²/8 + 3653.1143²/8) = -0.5341

df = ((s1²/n1 + s2²/n2)²)/[(s1²/n1)²/(n1-1) + (s2²/n2)²/(n2-1) ] = 9.632 = 10  

p-value = T.DIST(-0.5341, 10, 1) = 0.3025

Decision:  

p-value > α, Do not reject the null hypothesis  

Conclusion:  

There is not enough evidence to conclude that males speak fewer words in a day than females