Question

Cholesterol: An article in the Archives of Internal Medicine reported that in a sample of 243...

Cholesterol: An article in the Archives of Internal Medicine reported that in a sample of 243 men, 74 had elevated total cholesterol levels (more than 200 milligrams per deciliter). In a sample of 230 women, 49 had elevated cholesterol levels. Can you conclude that the proportion of men with elevated cholesterol levels is less than the proportion of women with elevated cholesterol levels? Let p1 denote the proportion of men with elevated cholesterol levels and p2 denote the proportion of women with elevated cholesterol levels. Use the a=0.10 level of significance and the P-value method with the TI-84 Plus calculator.

find p value:

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Answer #1

Solution:

Given:

Men:

n1 = 243

x1 = Number of men had elevated total cholesterol levels = 74

Women:

n2 = 230

x2 = Number of women had elevated cholesterol levels = 49

We have to test: if  the proportion of men with elevated cholesterol levels is less than the proportion of women with elevated cholesterol levels.

Level of significance = 0.10

p1 = the proportion of men with elevated cholesterol levels

p2 = the proportion of women with elevated cholesterol levels.

thus H0 and H1 are:

H0: p1 = p2 Vs H1: p1 < p2

Find p-value:

Use following steps in TI 84 plus calculator:

Press STAT and select TESTS

Under TESTS select 2-PropZTest

TI-84 Plus Silver Edition TEXAS INSTRUMENTS EDIT CALC TESTS 1: Z-Test... 2:T-Test... 3:2-SampZTest.... 4:2-SampTTest.... 5:1-

Enter numbers:

TI-84 Plus Silver Edition TEXAS INSTRUMENTS 2-ProPZTest X1:74 ni: 243 X2:49 12:230 P1:72 KPX >P2 Calculate Draw STAT PLOTF1 T

Click on Calculate and press Enter

TI-84 Plus Silver Edition TEXAS INSTRUMENTS 2-ProPzTest P1P2 z=2.267006318 P=.9883651159 15.364526749 A2=.2136434783 =.260042

p-value = 0.9883

Decision Rule:
Reject null hypothesis H0, if P-value < 0.10 level of significance, otherwise we fail to reject H0

Since p-value = 0.9883 > 0.10 level of significance, we fail to reject H0.

Conclusion:

At 0.10 level of significance, we do not have sufficient evidence to conclude that the proportion of men with elevated cholesterol levels is less than the proportion of women with elevated cholesterol levels.

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