Question

1. The military has two different programs for training aircraft personnel. A government regulatory agency has been commissioned to evaluate any differences that may exist between the two programs. The agency administers standardized tests to randomly selected groups of students from the two programs. The results of the tests for the students in each of the programs are as follows.

Military Training Program

n x s

Program A   50 85 10

Program B 50 87 8

a. Calculate a 99% confidence interval for the difference between the average scores of the two military programs. Interpret the interval.

b. Can the agency conclude that there is a difference in the average test scores of students in the two programs? Construct the 10 steps of hypothesis testing using α = 0.01 to answer the question.

10 Steps:

Step 1 (Define the hypotheses to be tested in plain English)

Step 2 (Select the appropriate statistical measure, such as the population mean, proportion, or
              variance.)

Step 3 (Determine whether the alternative hypothesis should be one-sided or two-sided.)

Step 4 (State the hypotheses using the statistical measure found in Step 2)

Step 5 (Specify α, the level of the test.)

Step 6 (Select the appropriate test statistic based on the information at hand and the
              assumptions you willing to make.)

Step 7 (Determine the critical value of the test statistic.)

Step 8 (Collect sample data and compute the value of the test statistic.)

Step 9 (Make the decision.)

Step 10 (State the conclusion in terms of the original question.)

Answer 1

a) Independent Samples Confidence Interval

μ₁ - μ₂ = (M₁ - M₂) ± ts_{(M1 - M2)}

Pooled Variance
s²_p = ((df₁)(s²₁) + (df₂)(s²₂)) / (df₁ + df₂) = 8036 / 98 = 82

Standard Error
s_{(M1 - M2)} = √((s²_p/n₁) + (s²_p/n₂)) = √((82/50) + (82/50)) = 1.81

Confidence Interval
μ₁ - μ₂ = (M₁ - M₂) ± ts_{(M1 - M2)} = 2 ± (2.63 * 1.81) = 2 ± 4.76

μ₁ - μ₂ = (M₁ - M₂) = 2, 99% CI [-2.76, 6.76].

You can be 99% confident that the difference between your two population means (μ₁ - μ₂) lies between -2.76 and 6.76.

_______________________________________________

b)

1)null hypothesis: there is no difference in the average test scores of students in the two programs

alternate hypothesis: there is a difference in the average test scores of students in the two programs

2) population mean

3) two sided

4)

Ho: μ1​ = μ2​

Ha: μ1​ ≠ μ2

5)alpha=0.01

6) ​t test for two independent samples for means

7)t=+/- 2.627

8) t= -1.104

9) null hypothesis is not rejected

10) conclusion there is not enough evidence to conclude that there is a difference in the average test scores of students in the two programs

detailed explaination given below---