Question

Question #5: A statistics teacher wants to see whether there is a statistically significant difference in the ages of day students and night students. A random sample of 31 students is selected from each group. The data are given below. Test the claim that there is difference in the mean ages of the two groups. Use a 0.01 Day Students: 22 24 24 23 19 19 23 22 18 21 21 18 18 25 29 24 23 22 22 21 20 20 20 27 17 19 18 21 20 23 26 Evening Students 18 20 25 23 20 24 25 23 23 23 19 25 20 21 24 19 23 27 23 24 23 24 20 21 20 24 21 21 20 28 27

Answer 1

Here the summary table for the day students and Evening students

Here sample mean age for day students $\bar x_d$ = 21.581

sample mean age for evening students $\bar x_e$   = 22.516

Standard deviation for day students s_d = 2.861

Standard deviation for evening students s_e = 2.541

Here

pooled standard deviation s_p = sqrt [(s_d² + s_e²)/2] = sqrt [(2.861² + 2.541²)/2] = 2.706

standard erorr of difference in means = sqrt [s_p² * (1/n₁ + 1/n₂)] = sqrt [2.706² * (1/31 + 1/31)] = 0.6873

Test statistic

t = ( $\bar x_d$ - $\bar x_e$ )/ se₀ = (21.581 - 22.516)/ 0.6873 = -1.3611

so at 0.01 significance level

t_critical = 2.66

so here t > t_critical so we will fail to reject the null hypothesis there is no difference in age of day students ad evening students.