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 in order to receive any credit. Please upload your completed assignment here. 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

Let µ₁ be Company A.

Let µ₂ be Company B.

The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ > µ₂

s² = (16-1)*1.1² + (21-1)0.9²/(16+21-2) = 0.9814

The test statistic, t = (5.2 - 4.6)/sqrt(0.9814*(1/16 + 1/21)) = 1.825

The df = 16 + 21 - 2 = 35

The p-value is 0.0383.

Since the p-value (0.0383) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that Company A retains its workers longer than Company B.