two statistics 1450 lab

Hypothesis Testing of Two Proportions

Lab Assignment _____ Name:

OBJECTIVES:

· To use Excel to calculate test statistics and p-values when comparing two sample proportions

· To use the p-value method to make conclusions.

· To use confidence intervals to test to determine if proportions from two populations are different.

EXCEL PROCEDURES:

Experiment 1:

Of 38 randomly selected moms of toddlers, 23 report sleeping more than 7 hours each night. Of 45 randomly selected dads of toddlers, 35 reported sleeping more than 7 hours/night. Is there evidence at the .05 level of significance to suggest that the proportion of moms that sleep more than 7 hours/night is different than the proportion of dads that get this much sleep?

a. Ho:

Ha:

Excel Procedure:

1. In cell A1 through A8 type x1, x2, n1, n2, phat1, phat2, pbar, and qbar.

2. In cell B1 through B4 enter the corresponding values for the variables in column A.

3. In cell B5 enter =B1/B3 and in cell B6 type =B2/B4.

4. In cell B7 enter =(B1+B2)/(B3+B4) and in cell B8 type =1-B7.

5. In cell D1 type “Z” and in cell D2 type “Area to the left of Z”.

6. In cell E1 type =(B5-B6)/SQRT(B7*B8/B3+B7*B8/B4). This will calculate the test statistic Z for this hypothesis test.

7. Select cell E2, then Formulas (the tab at the top of the Excel window)->More Functions->Statistical->NORM.S.DIST.

8. When the Function Arguments window opens select (or enter) cell E1 for Z.

9. In the Cumulative field type TRUE. This gives the area to the left of Z in the standard normal curve.

b. Test Statistic: __________________

c. Area left of z: ___________ Adjust this area to match the inequality in Ha in order to determine the p-value below. Show work here and check with your TI-84.

d. P-value: __________________

e. Conclusion (explain why using p-value method and interpret in context).

Experiment 2:

Of 38 randomly selected moms of toddlers, 23 report sleeping more than 7 hours each night. Of 45 randomly selected dads of toddlers, 35 reported sleeping more than 7 hours/night. Construct the Confidence Interval to determine if the proportion of moms that sleep more than 7 hours/night is different than the proportion of dads that get this much sleep.

a. Moms sample proportion: ___________

b. Dads sample proportion: ___________

c. Use the significance level (0.05) from Experiment 1 to determine the Confidence Level needed.

Excel Procedure:

1. In cell A10 through A16 type x1, x2, n1, n2, Confidence Level, phat1, and phat2.

2. In cell B10 through B16 enter the corresponding values for the variables in column A (be sure to enter your Confidence Level as a decimal).

3. In cell B15 enter =B10/B12 and in cell B16 type =B11/B13.

4. In cell D10 through D14 type Zc, ME, Samp Diff, CI Low, and CI High.

5. In cell E10 type =ABS(

6. Select Formulas (tab from the top of the Excel window)->More Functions->Statistical->NORM.S.INV.

7. In the probability field type (1-B14)/2 and select OK.

8. Close your ) for the ABS function.

9. In cell E11 type =E10*SQRT(B15*(1-B15)/B12+B16*(1-B16)/B13).

10. In cell E12 type =B15-B16.

11. In cell E13 type =E12-E11.

12. In cell E14 type =E12+E11.

d. Confidence Interval: _________________________________

e. Interpret the Confidence Interval in context.

f. Conclusion (explain why and interpret in context).

g. Is this conclusion consistent with your conclusion in Experiment 1? ______ Explain.

Experiment 3:

Of 75 randomly selected homeowners in Central Ohio, 52 say they generally trust their neighbors. Of 100 randomly selected apartment renters in Central Ohio, 66 say they generally trust their neighbors. Is there evidence at the 3% level of significance, to suggest that the proportion of Central Ohio homeowners that trust their neighbor is greater than the proportion for apartment renters?

a. Ho:

Ha:

Excel Procedure:

1. In cell A18 through A25 type x1, x2, n1, n2, phat1, phat2, pbar, and qbar (or copy/paste cells A1 thru A8).

2. In cell B18 through B21 enter the corresponding values for the variables in column A.

3. In cell B22 enter =B18/B20 and in cell B23 type =B19/B21.

4. In cell B24 enter =(B18+B19)/(B20+B21) and in B25 enter =1-B24.

5. Highlight cells D1-E2, Right click in the highlighted area and select Copy.

6. Select cell D18, right click in it and select Paste. This will fill cells D18 through E19 and will update the formulas from D1-E2 to use the appropriate cells for this experiment.

b. Test Statistic: __________________

c. Area left of Z: ___________ Adjust this area to match the inequality in Ha in order to determine the p-value below. Show work here and check with your TI-84.

d. P-value: __________________

e. Conclusion (explain why and interpret in context).

Copy and paste the table of results from your three hypothesis tests at the end of this lab.

Two Proportions Page 1