Question

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:

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-PropZTest... 382-PropZTest.... 7+Interval... STAT PLOTF1 TBLSETF2 FORMAT F3 CALC F4 TABLE F5 WINDOW ZOOM TRACE GRAPH 2ND CU MODE DEL ALPHA X.T.. STAT MATH APPS PRAWC PRGM VARS CLEAR

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 TBLSETF2 FORMAT F3 CALC F4 TABLE F5 Y WINDOW ZOOM TRACE GRAPH 2ND QUIT MODE INS DEL LIST STAT (OD ALDOR ALPHA TESTA MATH [email protected] ANGLE B APPS DRAWC PRGM DISTR VARS CLEAR

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 =.2600422833 STAT PLOTF1 TBLSETF2 FORMAT F3 CALC F4 TABLE F5 Y WINDOW ZOOM TRACE GRAPH 2ND ALDOR ALPHA TESTA MATH QUIT INS MODE DEL LINK LIST [email protected] STAT ANGLEB DRAW APPS PRGM DISTR VARS CLEAR

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.