Question

A data set about speed dating includes​ "like" ratings of male dates made by the female dates. The summary statistics are n=187 x=6.85 s=2.12 Use a 0.050 significance level to test the claim that the population mean of such ratings is less than 7.00 Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

Answer 1

Solution :

This is the left tailed test,  

The null and alternative hypothesis is ,

H0 :   = 7.00

Ha : < 7.00

Test statistic = t =

= ( - ) / s / n

= (6.85 - 7.00) / 2.12 / 187

Test statistic = t = -0.968

P(t < -0.968)

degrees of freedom = n - 1 = 187 - 1 = 186

P-value = 0.1672

= 0.05  

P-value >

Fail to reject the null hypothesis .