difference between students- stats and probability?

Question

A statistic teacher wanted to see whether there is a significant difference in the ages between day students and night students. A random sample of 35 students is selected from each group. The data are given below. Test the claim that there is no difference in age between the two groups. Use alpha ewual to 0.05.

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 23 26 30 25 21 25

Evening Students
18 23 25 23 21 21 23 24 27 31 24 20 20 23 19 25 24 27 23 20 20 21 25 24 23 28 20 19 23 24 20 27 21 29 30

Answer 1

This is a two sample Z-test of hypothesis (it can also be analyzed with a confidence interval, but a hyp. test is easier:
Ho: µ1 = µ2
Ha: µ1 not equal µ2
α = 0.05
Critical Z-value = ± 1.96
Calculations for Day Students: Xbar1 = 22.06, S1 = 3.16, S1² = 9.99
Calculations for Evening Students: Xbar2 = 23.29, S2 = 3.27, S2² = 10.69
Calculated Z = (Xbar1 - Xbar2)/(√((S1²/n1)+(S2²/n2))
= (22.06 - 23.29)/√((9.99/34)+(10.69/35)) = -1.23/√0.60 = -1.59
Decision: Because -1.59 is NOT in the critical area, we cannot reject the null hypothesis and conclude that we cannot prove a difference in ages if I've copied the data correctly.

Answer 2

v=(2-1)(35-1)=1.34=34
critical value from chi square table is 48,602

alpha=0.05

day students number must be 35 not 34
calculate expected value of each
Then calculate chi square and then compare it with 48,602