LAB 8: Hypothesis Testing for a Population Mean

Before you begin this lab, make sure that the Add-In component DDXL is available.

 To do this click on the Add-Ins button in Excel and look for DDXL on the far left hand side of your screen. If the DDXL feature is not shown, ask your instructor for help.

Purpose: In this lab, we will use Excel to test a hypothesis about a population mean.

Testing a Hypothesis about a Population Mean

To show this procedure, we will use the following example. The trend of thinner Miss America winners has generated charges that the contest encourages unhealthy diet habits among young women. Listed below are body mass indexes (BMI) for recent Miss America winners. Use a 0.01 significance level to test the claim that recent Miss America winners are from a population with a mean BMI less than 20.16, which was the average BMI for winners from the 1920s and 1930s.

19.5 20.3 19.6 20.2 17.8 17.9 19.1 18.8 17.6 16.8

In order to use Excel to test a hypothesis about a population mean, we will need to use the following steps. (You may assume a normal population distribution for this problem.)

1. Open a new worksheet.

2. Go to Save As and save this worksheet entitled “HypTestMean”.

3. Enter the data values into your worksheet. For this example, we will enter in the BMI values given above.

4. Click Add-Ins on the menu bar and select the DDXL option. Then select Hypothesis Tests.

5. In the Hypothesis Test dialog box, choose 1 Var t Test. (Make sure that the box in front of the First Row is variable names is unchecked if you did not include the variable name in your worksheet.) Click on the pencil icon under Quantitative Variable and list the range of cells that include your data. For this example, type in “A1:A10”. Click OK.

6. A dialog box will open that requires more information.

a) Click on Set µθ. Enter the value of the population mean that can be found in the claim. For this example it is 20.16. Click OK.

b) Set the significance level by clicking on the appropriate value. For this example, click on .01.

c) Select the alternative hypothesis. For this problem click on µ < µθ since the problem involves less than 20.16. d) Click on Compute.

7. A t Test dialog box displays the information needed for performing a test of hypothesis for a mean.

8. Click on the title bar of the box entitled “A1:A10 tTest”. From the Edit menu choose Copy Window. Then go to your Excel worksheet and right click and Paste in the window.

9. Save your worksheet.

Use your results and DDXL to answer the following questions.

1. Explain what the different results that are given in your Test Summary section represent.

2. The Test Results section tells us to reject the null hypothesis for this problem. Why did DDXL decide to reject the null?

3. Explain how you could use the traditional method to test the claim that the mean BMI is less than 20.16. What is missing from the results to use this method? To find this missing result, use the following steps.

a) Select your worksheet.

b) Choose Formulas from the menu bar, More Functions, Statistical, T.INV.2T.

c) In the T.INV.2T dialog box, type in “probability” the significance level, α , for a two- tailed test, or 2α for a one tailed test (as above). Then type in the degrees of freedom, which is found by calculating n-1. Click OK.

d) The value will be placed in your worksheet. For this example, we have a left tailed case, which means that we will have to manually make this value negative.

e) Include the value of the missing result in your write up.

4. Using the results obtained, write an interpretation for this hypothesis test.

5. Do recent winners have a significantly lower average BMI than those in the 1920s and 1930s? Explain.

6. A simple random sample of pages from Merriam-Websters Collegiate Dictionary is obtained. Listed below are the numbers of words defined on those pages. Given that this dictionary has 1,459 pages with defined words, the claim that there are more than 70,000 defined words is the same as the claim that the mean number of defined words on a page is greater than 47.97807 (i.e. 70,000/1,459). (You may assume a normal population distribution for this problem.) 51 63 36 43 34 62 73 39 53 79

a) Use this information and DDXL to test the claim that the mean number of defined words on a page is greater than 47.97807.

b) Copy and paste your results into your Excel worksheet under your previous work.

c) Find the t critical value using steps from question 3.

d) Write an interpretation for your hypothesis test.

e) What does the result suggest about the claim that there are more than 70,000 defined words in the dictionary? Explain using the results of your hypothesis test.

Be sure to include the following in your lab report:

A. Cover sheet with a summary of the lab you did. It should be one to two paragraphs.

B. Answer all the questions stated above on the answer sheets provided to get full credit.

C. Attach the worksheet that you were asked to print that includes the results from two different hypothesis tests.