Question

Two random samples of 40 students were drawn independently from two populations of students. Assume their aptitude tests are normally distributed and assume the variances of each sample are equal. The following statistics regarding their scores in an aptitude test were obtained: x with bar on top subscript 1 equals 76 comma space s subscript 1 equals 8 comma space x with bar on top subscript 2 equals 73 comma space s subscript 2 equals 7. Test at the 5% significance level to determine whether we can infer that the two population means differ. What is the conclusion from your test? a. None of these answers are correct b. Do not reject the null hypothesis c. Do not accept the null hypothesis d. Accept the alternate hypothesis e. Reject the null hypothesis

Answer 1

b. Do not reject the null hypothesis

Explanation:

Given that two random samples of 40 students were drawn independently from two populations of students. Assuming equal variances

we have the following data.

Sample 1

Mean:

76

Standard deviation:

8

Sample size:

40

Sample 2

Mean:

73

Standard deviation:

7

Sample size:

40

`H_0: \bar x_1=\bar x_2\\H_a:  \bar x_1\\eq \bar x_2`

Difference -3.000

Standard error 1.681

95% CI -6.3462 to 0.3462

t-statistic -1.785

DF 78

Significance level P = 0.0782

Since p value >0.05,

b. Do not reject the null hypothesis