Question

Problem # 9: Nationwide, the average salary of actuaries who achieve the rank of Fellow is $151,000. An insurance executive wants to see how this compares with Fellows within his company. He checked the salaries of 12 Fellows and finds the average salary to be $156,000 with the standard deviation of $10,000. Can he conclude that Fellows in his company make more than the national average, using 0.01 level of significance? Find the test value.

Answer 1

Solution :

Given that,

Population mean = = 151000

Sample mean = = 156000

Sample standard deviation = s = 10000

Sample size = n = 12

Level of significance = = 0.01

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 151000

Ha: 151000

The test statistics,

t =( - )/ (s /n)

= ( 156000 - 151000 ) / ( 10000/ 12 )

= 1.732

P-value = 0.1112

The p-value is p = 01112 > 0.01. it is concluded that fail to reject the null hypothesis.

Conclusion :

It is concluded that fail to reject the null hypothesis. Therefore, there is not enough evidence to claim that Fellows in his company make more than the national average, using 0.01 level of significance.