Question

A sociologist thinks that middle school boys spent less time studying in 1981 than middle school boys do today. A study was conducted in 1981 to find the time that middle school boys spent studying on weekdays. The results (in minutes per weekday) are shown below.

31.9 35.4 28.0 39.1 30.5 31.9 33.0 29.6 35.7 30.2 38.8 35.9 37.1 36.2 32.6 36.9 24.2 28.5 28. 7 41.1 33.8 32.1 28.7 35.4 36.6. 34.3 35.5 34.2 33.8 25.3 27.7 21.9 30.0 36.8 26.9

Recently, a similar study was conducted. The results are shown below.

44.7 54.6 41.1 46.7 43.0 47.2 58.0 51.0 41.1 49.6 47.1 45.5 52.8 49.4 47.2 51.5 55.0 44.7 42.2 52.0 46.6 42.9 48.7 50.0 47.9 51.3 39.0 45.6 49.8 54.4 54.8 40.2 45.4 48.6 50.0

  At a = 0.03, can you support the sociologist’s claim? Note that you are expected to

1. identify the claim and state H0 and Ha
2. find the critical value(s)/p-values and identify the rejection region(s),
3. find the standardized test statistic z, and sketch a graph
4. decide whether to reject or fail to reject the null hypothesis, and interpret the decision in the context of the original claim.
5. Obtain a 97% confidence interval and interpret your results.

Answer 1

d. Since from (c) we see that observed value of z (blue point) falls in critical region, we reject null hypothesis at 3% level of significance and conclude that there is sufficient evidence to conclude that the middle school boys spent less time studying in 1981 than middle school boys do today.

e.

the middle school boys spent less time studying in 1981 than middle school boys do today..