Question

Test the claim that the mean IQ score of Statistics professors is greater than 118. Assume that you have the following sample data:

n = 50 teachers

x = 120

s = 12

significance level = 0.05

Answer 1

Solution :

Given that,

Population mean = = 118

Sample mean = = 120

Sample standard deviation = s = 12

Sample size = n = 50

Level of significance = = 0.05

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: 118

Ha: 118

The test statistics,

t = ( - )/ (s/)

= ( 120 - 118 ) / ( 12 /50)

= 1.179

Critical value of  the significance level is α = 0.05, and the critical value for a right-tailed test is

= 1.677

Since it is observed that t = 1.179 < = 1.677 it is then concluded that the null hypothesis is fails to reject.

P- Value = 0.1221

Using the P-value approach: The p-value is p = 0.1221 > 0.05 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 118, at the 0.05 significance level.