We are interested in comparing the efficiencies of two teaching methods. Six students were taught using each

Fantastic news! We've Found the answer you've been seeking!

Question:

We are interested in comparing the efficiencies of two teaching methods. Six students were taught using each method and their performance scores are shown in the following table.

Method 1	Method 2
79	71
66	43
57	58
91	78
42	20
59	56

Assume that the twelve students are different. Perform the appropriate analysis regarding the comparison of the efficiencies of two teaching methods by using only descriptive statistics in R (i.e. mean() and var()). In particular, state the null and alternative hypothesis, conduct the test at alpha level 0.01, derive a symmetric 99% confidence interval for the parameters of interest. Give interpretations for all relevant quantities.

Perform the analysis from part a) in R and confirm your results.

Assume that the same six students were tested twice after being taught each method. Perform the appropriate analysis regarding the comparison of the efficiencies of two teaching methods by using only descriptive statistics in R. In particular, state the null and alternative hypothesis, conduct the test at alpha level 0.01, derive a symmetric 99% confidence interval for the parameters of interest. Give interpretations for all relevant quantities.

Perform the analysis from part c) in R and confirm your results.

Test the hypothesis that the average performance score for students taught using Method 1 is 80. Construct a symmetric 90% confidence interval for the population average score.

Test the hypothesis that the variance of the performance scores for students taught using Method 1 is 100. Construct a 95% confidence interval for the population variance.

Compare the results in parts a) and c). Comment on which one you would choose if the data collection process is not a problem. What would be an even better approach to collect data in an attempt to answer the question of interest?