and selecting the difference variable you created. Sketch the plot. Does it show evidence of a normal population of differences? If not, can we still proceed with the test, and why?3.Compute the Test Statistic and Calculate the p-value Test Statistic Method 1: Using R to create a variable for the differences and performing a single-sample t-test. a.Now, we will compute summary statistics of the difference variable created in 2b. Go to Statistics > Summaries > Numerical summariesto generate these, making sure you select your difference variable, and fill out the table below. Be sure to check the standard error option under the Statistics tab. Summary Statistics Mean diff (࠵࠵{) Std. Dev (࠵࠵࠵࠵) Sample size (࠵࠵) Std. Error (࠵࠵. ࠵࠵. ~࠵࠵{°) b.Now, try conducting a one mean test on the difference variable we created. This can be found by going to Statistics > Means > Single-sample t-test. Don’t forget to specify the correct direction for the alternative hypothesis (see your hypotheses from Part 1) One Sample T Results for the Differences t df p-value *Think about why the p-value is so large c.Our observed sample mean difference (࠵࠵̅) is ________________ standard errors below the hypothesized population mean difference of zero. What is this an interpretation of? d.What is the distribution of the test statisticif the null hypothesis is true? ___________________ Note: This is not the same as the distribution of the population that the data were drawn from, and will be the model used to find the p-value.

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Lab Workbook Page 66 Method 2: Using R to perform a paired t test without creating a new variable for the differences. a.Generate the t-test output using Statistics > Means > Paired T Test. Select the two variables (R defaults to test ‘First variable’ minus ‘Second variable’), and specify the correct direction for the alternative hypothesis (see your hypotheses from Part 1) in the Options tabs. Use the output to fill out the following output table for this test. Paired T Results t df p-value Note: The results you obtain from Method 1should be the same as the results in Method 2. b.Verify that your results from Method 1 are consistent with your results from Method 2. Thep-value a.Draw a picture of the p-value, with labels for the distribution and x-axis. b.Provide an interpretation of the p-value in context. 4.Evaluate the p-value and conclusion a.What is your decision at a 5% significance level? Reject H0Fail to Reject H0Remember:Reject H0óResults statistically significant Fail to Reject H0 óResults not statistically significant b.What is your conclusion in the context of the problem? Note: Conclusions should always include a reference to the population parameter of interest. Conclusions should not be too strong; you can say that you have sufficient evidence, but do NOT say that we have provenanything true or false.

Lab Workbook Page 67 Lab 8: Comparing Two Means Objective:In this lab, you will learn an important statistical technique that will allow you to compare two populations with respect to their means by looking at μ1-μ2.