Question

In clinical trials of the allergy medicine Clarinex (5 mg), it was reported that 50 out of 1655 individuals in the Clarinex group and 31 out of 1652 individuals in the placebo group experienced dry mouth as a side effect of their respective treatments.

Test the hypothesis that a greater proportion of individuals in the experimental group experienced dry mouth compared to the individuals in the control group at the level of 5% significance.

Null Hypothesis:
Alternate Hypothesis:

P-value:

Conclusion:

Interpretation:

Construct a 95% confidence interval for the difference between the two population proportions Experimental – Control. Explain what it means.

Answer 1

Test and CI for Two Proportions

Sample   X     N Sample p
1       50 1655 0.030211
2       31 1652 0.018765

Difference = p (1) - p (2)
Estimate for difference: 0.0114463
95% lower bound for difference: 0.00261162
Test for difference = 0 (vs > 0): Z = 2.13 P-Value = 0.017

Null Hypothesis: p1 = p2
Alternate Hypothesis: p1 > p2

P-value: 0.017

Conclusion: p-value < 0.05 , we fail to reject the null hypothesis

Interpretation: there is sufficient evidence that a greater proportion of individuals in the experimental group experienced dry mouth compared to the individuals in the control group at the level of 5% significance.

Construct a 95% confidence interval for the difference between the two population proportions Experimental – Control.

95% CI for difference: (0.000919122, 0.0219736)