# Hypothesis Testing of Proportions

awson and Jick [1976] compare drug prescription in the United States and Scotland.

(a) In patients with congestive heart failure, two or more drugs were prescribed in 257 of 437 U.S. patients. In Scotland, 39 of 179 patients had two or more drugs prescribed. Test the null hypothesis of equal proportions giving the resulting p- value. Construct a 95% confidence interval for the difference in proportions.

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Biostatistics

Awson and Jick [1976] compare drug prescription in the United States and Scotland.

(a) In patients with congestive heart failure, two or more drugs were prescribed in 257 of 437 U.S. patients. In Scotland, 39 of 179 patients had two or more drugs prescribed. Test the null hypothesis of equal proportions giving the resulting p- value. Construct a 95% confidence interval for the difference in proportions.

Answer

The null hypothesis tested is

H0: There is no significant difference in the proportion of patients had two or more drugs prescribed in the United States and Scotland (P1 = P2)

The alternative hypothesis is

H1: There is significant difference in the proportion of patients had two or more drugs prescribed in the United States and Scotland (P1 â‰ P2)

The Test Statistic used is

where

Here p1 = 257/437 = 0.588100686, p2 = 39/179 = 0.217877095, n1 = 437, n2 = 179

Now = 0.480519481

Therefore, = 8.350276088

Rejection criteria: Reject the null hypothesis, if the observed significance (p-value) is less than the significance level 0.05.

P-value = P ( > 8.350276088) = 0

Conclusion: Reject the null hypothesis, since the observed significance (p-value) is less than the significance level 0.05. The sample provides enough evidence to conclude that there is significant difference in the proportion of patients had two or more drugs prescribed in the United States and Scotland.

Details

Z Test for Differences in Two Proportions

Data

Hypothesized Difference 0

Level of Significance 0.05

Group 1

Number of Successes 257

Sample Size 437

Group 2

Number of Successes 39

Sample Size 179

Intermediate Calculations

Group 1 Proportion 0.588100686

Group 2 Proportion 0.217877095

Difference in Two Proportions 0.370223592

Average Proportion 0.480519481

Z Test Statistic 8.350276088

Two-Tail Test

Lower Critical Value -1.959963985

Upper Critical Value 1.959963985

p-Value 0

Reject the null hypothesis

95% confidence interval is given by,

, where p1 = 257/437 = 0.588100686, p2 = 39/179 = 0.217877095, n1 = 437, n2 = 179, = 1.959963985

Therefore, required confidence interval is

= (0.294154929, 0.446292254)

Thus with 95% confidence we can claim that the difference in proportions is within (0.294, 0.446).

Details

Confidence Interval Estimate

of the Difference Between Two Proportions

Data

Confidence Level 95%

Intermediate Calculations

Z Value -1.959963985

Std. Error of the Diff. between two Proportions 0.038811255

Interval Half Width 0.076068662

Confidence Interval

Interval Lower Limit 0.294154929

Interval Upper Limit 0.446292254

https://brainmass.com/statistics/hypothesis-testing/hypothesis-testing-proportions-454184