Question

A study using two random samples of 35 people each found that the average amount of time those in the age group of 26-35 years spent per week on leisure activities was 39.6 hours, and those in the age group of 46-55 years spent 35.4 hours. Assume that the population standard deviation for those in the first age group found by previous studies is 6.3 hours, and the population standard deviation of those in the second group found by previous studies was 5.8 hours.

a. At an alpha of 0.05, can it be concluded that there is a significant difference in the average times each group spends on leisure activities?

b. Using this data find the 95% confidence interval of the difference between the means.

Answer 1

a)

   

The test statistic is

   

  

At = 0.05, the critical values are +/- z_0.025 = +/- 1.96

Since the test statistic value is greater than the positive critical value (2.90 > 1.96), so we should reject the null hypothesis.

At 0.05 significance level, there is sufficient evidence to conclude that there is a significant difference in the average times each group spends on leisure activities.

b) For the 95% confidence interval, the critical value is z_0.025 = 1.96

The 95% confidence interval is