1. Statistics at a certain college has been historically taughtat two times: at 8 am and at 4 pm.
A random sample of 150 students that took the morning classresults in a mean score of 81.2 points, with a standard deviationof 18 points, and a random sample of 150 students that took theafternoon class results in a mean score of 76.4 points and astandard deviation of 21 points. For this problem, assume that thesample sizes are large enough so that the sample standarddeviations (S) are good approximations for the unknown populationstandard deviations (σ).
a. Compute a 95% confidence interval for the mean score for allstudents taking statistics at 8 am.
b. Compute a 95% confidence interval for the mean score for allstudents taking statistics at 4 pm.
c. Based on the confidence intervals, is there strong evidenceto support the claim that the morning classes do better instatistics? Explain.
2. A poorly written research paper states a confidence intervalfor the mean reaction time to an experiment as 83.6 ± 11.515seconds, but forgot to mention what the confidence level was.However, the paper did say that the population standard deviationis σ = 35, and the sample size was n = 25.
a. What was the confidence level used for the confidenceinterval stated in the paper? b. Using the same sample results, howcould you lower the margin of error to below 10 seconds?
