Question

1. Statistics at a certain college has been historically taught at two times: at 8 am and at 4 pm.

A random sample of 150 students that took the morning class results in a mean score of 81.2 points, with a standard deviation of 18 points, and a random sample of 150 students that took the afternoon class results in a mean score of 76.4 points and a standard deviation of 21 points. For this problem, assume that the sample sizes are large enough so that the sample standard deviations (S) are good approximations for the unknown population standard deviations (σ).

a. Compute a 95% confidence interval for the mean score for all students taking statistics at 8 am.

b. Compute a 95% confidence interval for the mean score for all students taking statistics at 4 pm.

c. Based on the confidence intervals, is there strong evidence to support the claim that the morning classes do better in statistics? Explain.

2. A poorly written research paper states a confidence interval for the mean reaction time to an experiment as 83.6 ± 11.515 seconds, but forgot to mention what the confidence level was. However, the paper did say that the population standard deviation is σ = 35, and the sample size was n = 25.

a. What was the confidence level used for the confidence interval stated in the paper? b. Using the same sample results, how could you lower the margin of error to below 10 seconds?

Answer 1

a)

Morning class result:

Given:

n = 150, = 81.2, S = 18, = 0.05

Degree of freedom =n-1 = 150-1 = 149

Critical value:

          ................Using t table

95% Confidence interval:

b)

Afternoon class result:

Given:

n = 150, = 76.4, S = 21, = 0.05

Critical value:

          ................Using t table

95% Confidence interval:

C)

Interval for population mean in morning classes are larger than afternoon classes.

So, There is strong evidence to support the claim that the morning classes do better in statistics