Question

Life insurance experts have been claiming that the average worker in the city of Cincinnati has no more than $25,000 of personal life insurance. An insurance researcher believes that this is not true and sets out to prove that the average worker in Cincinnati has more than $25,000 of personal life insurance. To test this claim, she randomly samples 100 workers in Cincinnati and interviews them about their personal life insurance coverage. She discovers that the average amount of personal life insurance coverage for this sample group is $26,650. The population standard deviation is $12,000.

Question:

a. If instead you were testing a null hypothesis stating that the average of the population is $25,000 against an alternative hypothesis that it is not equal to $25,000, where would the critical values lie assuming an = 10%?

b. Explain the meaning of the critical values obtained from question above and how you would use these in hypothesis testing.

Answer 1

(a)

= 0.10

From Table, critical values of Z = 1.64

So,

the critical values lie

1.64

(b)

(i)

The meaning of the critical values obtained from question above :

The critical values of Z = 1.64 corresponding to significance level = = 0.10 is the area in the tails of the Standard Normal Curve on either side of the mid value.

(ii)

Twst Statistic is given by:

Since calculated value of Z = 1.375 is less thancritical value of Z = 1.64, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that the average of the population is not equal to $25,000