Let's return to the widget company from Lab 4. The company has two machines that make widgets. The two machines should be making widgets with the same mean length. You are asked to perform a quality control check to verify if this is true. You pull samples of 50 widgets from each machine. The mean length of the widgets made by Machine 1 is 10.03 inches. The sample standard deviation is 0.07 inches. The mean length of the widgets made by Machine 2 is 10.01 inches and the sample standard deviation is 0.05 inches. Assume the population standard deviations are equal. Use a significance level of 0.05

3. What is the degrees of freedom for this test?

5. What is the value of the critical value(s). If two-tailed test, with +/- values, just enter the positive value here. Round to three decimal places.

6. Compute the test statistic (round to three decimal places, as needed)

9. Re-do the hypothesis test assuming that the population standard deviations are NOT equal. What is the p-value? (Round to 3 decimal places)