Project for inference about the mean

The purpose of this project is to allow you to become familiar with the process of using actual data to do tests of hypotheses and to find confidence intervals. The data for this project came from stat200 class surveyed a few semesters ago. They recorded:

  • their sex (0 for male, 1 for female)
  • GPA
  • height and weight
  • left and right arm length
  • left and right foot length

The data set comprises the population of interest. You are going to draw random samples from the population (simple random sampling with replacement) to do inferences about the population means.

Part a) Confidence interval for the mean of one variable that you are interested in. For example, the GPA of the class of stat 200 students. We want to draw inference about the population mean by a random sample with replacement from the population. To see the effect of sample size on the inference, repeat the procedure three times using random samples of sizes 25, 40 and 64 respectively. Since for the purpose of this project one can also find out the population mean, you can see how well the sample mean estimates the population mean and whether the confidence intervals contain the actual population mean. Comment about it in your report.

Part b) Test of two means. You should select a hypothesis you are interested in testing and then use a test of two means to test this hypothesis. For example, you may be interested in testing whether the GPA of females is higher than that of males in that class. One is going to draw the inference by using a random sample with replacement of size 25 from each group. Report the p-value of the test. Perform the test using a significance level a = .05. Use graphical methods to present the two populations of interest.

Part c) Paired difference test. You should select another hypothesis that you are interested in and select it in such a way that the paired difference test is appropriate. For example, suppose one is interested in testing whether the right arm length is equal to left arm length. Then, in this case, a paired difference test is appropriate. Draw inference by using a random sample with replacement of 25 from each group. Perform the test using a significance level a that you choose.

Report Guideline:

Three to four students should work in a group and hand in one report. The report should be typed and stapled on the left edge. Minitab output should be included. There should be a cover page with your names, student ID numbers and the project title. For each of the three parts, provide conclusions.