Question

Test H0: m £ 8 versus HA: m > 8, given a = 0.01, n = 25, X ̅ = 8.13 and s = 0.3. Assume the sample is selected from a normally distributed population.

Answer 1

Solution :

This is a right tailed test.

The test statistics,

t = ( - )/ (s/)

= ( 8.13 - 8 ) / ( 0.3 /25)

= 2.167

Critical value of  the significance level is α = 0.01, and the critical value for a right-tailed test is

= 2.492

Since it is observed that t = 2.167 <   = 2.492 it is then concluded that the null hypothesis is fails to reject.

p-value = 0.0202

The p-value is p = 0.0202 > 0.01, 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 μ is greater than 8, at the 0.01 significance level.