# Hypothesis Testing of Proortions: Lovastatin

Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study, researchers gave lovastatin to 2,325 people and an inactive substitute to 2,081 people (average age 58). After 5 years, 57 of the lovastatin group had suffered a heart attack, compared with 97 for the inactive pill.

(a) State the appropriate hypotheses. (b) Obtain a test statistic and p-value.

Interpret the results at ? = .01.

(c) Is normality assured?

(d) Is the difference large enough to be important?

(e) What else would researchers need to know before prescribing this drug widely?

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Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study, researchers gave lovastatin to 2,325 people and an inactive substitute to 2,081 people (average age 58). After 5 years, 57 of the lovastatin group had suffered a heart attack, compared with 97 for the inactive pill.

Answers

(a) State the appropriate hypotheses.

The null hypothesis tested is

H0: There is no significant difference in proportion of heart attack in the two groups.

The alternative hypothesis is

H1: The proportion of heart attacks in the lovastatin group is less than the inactive pill group.

(b) Obtain a test statistic and p-value. Interpret the results at Î± = .01.

The test Statistic used is

where

Here n1 = 2325, x1 = 57, n2 = 2081, x2 = 97, p1 = 57/2325 = 0.024516129, p2 = 97/2081 = 0.046612205

That is, = 0.034952338

Therefore, = -3.986832082

P-value = P (Z < -3.986832082) = 3.34807E-05

Rejection criteria: Reject the null hypothesis, if the observed significance (p value) is less than the significance level (0.01)

Conclusion: Reject the null hypothesis, since the observed significance (p value) is less than the significance level (0.01). The sample provides enough evidence to support the claim that the proportion of heart attacks in the lovastatin group is less than the inactive pill group.

Details

Z Test for Differences in Two Proportions

Data

Hypothesized Difference 0

Level of Significance 0.01

Group 1

Number of Successes 57

Sample Size 2325

Group 2

Number of Successes 97

Sample Size 2081

Intermediate Calculations

Group 1 Proportion 0.024516129

Group 2 Proportion 0.046612206

Difference in Two Proportions -0.022096077

Average Proportion 0.034952338

Z Test Statistic -3.986832082

Lower-Tail Test

Lower Critical Value -2.326347874

p-Value 3.34807E-05

Reject the null hypothesis

(c) Is normality assured?

Since the sample size is fairly large, we can assume that the normality assumption is valid for the data.

(d) Is the difference large enough to be important?

If the difference between the two proportions is large, it is very likely that there is significant difference between the control group and experiment group.

(e) What else would medical researchers need to know before prescribing this drug widely?

The researchers should ensure that all other factors are under similar for both the experimental groups and control group.

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