I am having throuble finding the critical value for the foloowing two problmes..

Question

I am having throuble finding the critical value for the foloowing two problmes...

-A company found that 27 out of 150 of its products were defective after retraining its employees. If the company normally has a 40% defective product rate, find the critical value to determine if retraining the employees helped to minimize the number of defective products. (My answer was 1.618, but was marked incorrect)

-A teacher gives 200 students a study guide for a test and the average score was 90 with a standard deviation of 6. She did not give the other 200 students a study guide and their average score was 70 with a standard deviation of 8. Find the critical value to determine whether or not the study guide helped students to increase their test score. (Ay answer was 1.649, but was marked incorrect)

Showing me how to work out these problems would be great. When using the graphing calculator would you please explain what you are typing in. Thank you!

Explanation / Answer

Problem on defectives

Here the hypothesis is: H0: p = 0.40   Vs HA: p < 0.40. For this hypothesis, the test statistic has Normal Distribution. Hence, the critical value would be 1.645 for 5% level of significance, and 2.575 for 1% level of significance.

Problem on test score

Here the hypothesis is: H0: µ1 = µ2   Vs HA: µ1 > µ2. For this hypothesis, the test statistic has t-Distribution with degrees of freedom = 2n – 2 = 200 – 2 = 198. Hence, the critical value would be 1.645 for 5% level of significance, and 2.575 for 1% level of significance.

DONE

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