QUESTION: 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. Determine whether or not the study guide helped students to increase their test score.

SHOW ME HOW I WOULD DO IT IN THIS WAY:

EX:

Step 1: Find the difference in the sample mean scores. 88-80 = 8 Step 2: Write the null and alternative hypotheses. H₀ = The study guide has no effect on student test scores or population mean₁ = population mean₂ or population mean₁ - population mean₂ = 0 H₁ = The study guide has an effect on student test scores or population mean₁ population mean₂ or population mean₁ - population mean₂ 0 Step 3:Calculate the standard deviation for the difference of the sample means. To do this we need to find the variance (square the standard deviation for each sample) and divide it by n for each sample then add the two values together and take the square root. [(2²)/100 + (3²)/100] = [4/100 + 9/100] = 13/100 = .13 =.36

Step 4:Assume that the null hypothesis is true and find the z-score using the difference of the means.

z = (8-0)/.36= 22.22 Subtract the test statistic from the difference of the means and then divide by the standard deviation to find the z-score. Since this z-score is extreme, we must reject the null hypothesis and conclude that the study guide has an effect on student test scores.