Question

A population is expected to have a mean of 50. A sample of size 64 is extracted and its mean is 55 with a standard deviation of 32. Required to test the claim at 95% confidence that the population mean is greater than 50. What is the P_value?

Answer 1

Solution :

Given that,

Population mean = = 50

Sample mean = = 55

Sample standard deviation = s = 32

Sample size = n = 64

Level of significance = = 0.05

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 50

Ha: 50

The test statistics,

t = ( - )/ (s/)

= ( 55 - 50 ) / ( 32 / 64 )

= 1.25

P-value = 0.108

It is concluded that p-value = 0.108 > 0.05 , the null hypothesis is fails to reject.

It is concluded that the null hypothesis Ho is fails to rejected. Therefore, there is not enough evidence to claim that the

population mean μ is greater than 50, at the 0.05 significance level.