Question

A study using two random samples of 35 people found the average amount of time spent on leisure activities for a the group in their 20s was 39.6 hours. The population standard deviation is 6.3 hours. The average time for a group in their 30s was 35.4 hours, and the population standard deviation was 5.8 hours. At LaTeX: \alphaα=0.05, is there a difference in the average times? (Let 1 = group in 20s and 2 = group in 30s) The correct TV is ________.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ1 = μ2
Alternative Hypothesis, Ha: μ1 ≠ μ2

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(39.69/35 + 33.64/35)
sp = 1.4475

Test statistic,
z = (x1bar - x2bar)/sp
z = (39.6 - 35.4)/1.4475
z = 2.90

P-value Approach
P-value = 0.0037
As P-value< 0.05, reject null hypothesis.

Reject Ho - mean times are different