Question

0.2 point for writing the hypothesis in symbolic form.

0.2 point for determining the value of the test statistic.

0.2 point for finding the critical value OR the p-value.

0.2 point for determining if you should reject the null hypothesis or fail to reject the null hypothesis.

0.2 point for writing a conclusion addressing the original claim.

All work must be shown

A study is done to test the claim that Company A retains its workers longer than Company B. Company A samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company B samples 21 workers, and their average time with the company is 4.6 years with a standard deviation of 0.9. The populations are normally distributed.

Answer 1

n1 = 16

= 5.2

s1 = 1.1

n2 = 21

= 4.6

s2 = 0.9

Claim: Company A retains its workers longer than Company B.

The null and alternative hypothesis is

For doing this test first we have to check the two groups have population variances are equal or not.

Null and alternative hypothesis is

Test statistic is

F = largest sample variance / Smallest sample variances

F = 1.1^2 / 0.9^2 = 1.21/0.81 = 1.494

Degrees of freedom => n1 - 1 , n2 - 1 => 16 - 1 , 21 - 1 => 15 , 20

Critical value = 2.203    ( Using f table)

Critical value > test statistic so we fail to reject null hypothesis.

Conclusion: The population variances are equal.

So we have to use here pooled variance.

Test statistic is

Degrees of freedom = n1 + n2 - 2 = 15 + 21 - 2 = 34

Critical value = 1.697   ( Using t table)

| t | > critical value we reject null hypothesis.

Conclusion:

Company A retains its workers longer than Company B.