# Statistics: Sex, Weight, GPA, Smoker and Arm and Leg Length

1) 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.

2) 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.

3) Regression and correlation. Pick any two columns that have a correlation coefficient greater than 0.6 or less than -0.6. Make sure to pick the one with the highest absolute value.

a. Draw the scatter diagram of Y against X, and explain any noted significance.

b. Compute correlation coefficient (? or r), and what do you find? Make sure to explain thoroughly what you mean.

c. Obtain a and b of the regression equation defined as Y = a + b X, and the Coefficient of Determination (r2) from the Excel regression output, what can you tell? What is the relationship between r2 and ??

d. Compute the above statistics in 4) step by step using SXiYi, SXi, SYi, SXi2, SYi2 from Excel, and compare them with the results in C).

e. Draw the fitted regression line on the scatter diagram, obtain the residuals and plot them on the scatter diagram too. Explain your findings.

f. Write a paragraph or so on any observations you may have on the data, regression estimates or the regression residuals;

g. Calculate the additional y values for at least five other x values that do not appear in our data. Include that information in your report above and comment on whether you believe the calculate y value seems realistic and consistent with the other information you have calculated in each of the parts above..

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#### Solution Preview

Test of Two Means:

We are interested in testing whether the GPA of females is higher than that of males in that class.

Null Hypothesis: The mean GPA of females is lower than or equal to the mean GPA of males in the class.

H0: u_f <= u_m

Alternate Hypothesis: The mean GPA of females is higher than the mean GPA of males in the class.

H1: u_f > u_m

The test method used is two-sample t-test for the mean. Level of significance used is ? = 0.05. Random samples with replacement of size 25 have been drawn from each group for the analysis. The t-test, assuming unequal variances, has been performed in EXCEL.

t-Test: Two-Sample Assuming Unequal Variances (see attached)

As the alternate hypothesis, H1: u_f > u_m the given test is a one-tailed test.

Decision Rule: Reject H0, if t-stat > 1.67722

The t-statistic (1.99358) is greater than t-critical ...

#### Solution Summary

This solution sets up the test of two means, paired difference test, and regression and correletaion. This solution is completed in the attached Excel file and discussed in the attached Word file.