Question

A data set about speed dating includes​ "like" ratings of male dates made by the female dates. The summary statistics are n=189​, x bar =6.89​, s=2.21. Use a 0.10 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 :

Given that,

Population mean = = 7

Sample mean = = 6.89

Sample standard deviation = s = 2.21

Sample size = n = 189

Level of significance = = 0.10

The null and alternative hypothesis is,  

Ho: 7

Ha: 7

The test statistics,

t = ( - )/ (s/)

= ( 6.89 - 7 ) / ( 2.21 /189 )

= -0.684

P- Value =  0.2473

The p-value is p = 0.2473 0.10, it is concluded that the null hypothesis is fails to reject.

Conclusion :

It is concluded that the null hypothesis Ho is fails to reject. Therefore, there is not enough evidence to claim that the population mean of such ratings is less than 7.00, at the 0.10 significance level.