Final answer:
To test the manufacturer's claim, a hypothesis test comparing two proportions is performed. The null hypothesis is that the proportion of Seldane-induced drowsiness is less than or equal to the placebo group. At a 5% level of significance, the decision to reject or fail to reject the null hypothesis is based on the p-value obtained from the test statistic.
Step-by-step explanation:
To test the claim that the population proportion of Seldane users who experience drowsiness is less than or equal to the population proportion of placebo users who experience drowsiness, we can conduct a hypothesis test for the difference in two proportions using the given data.
First, we specify the null hypothesis (H0) and the alternative hypothesis (Ha):
- H0: p1 ≤ p2 (The proportion of Seldane users experiencing drowsiness is less than or equal to that of placebo users)
- Ha: p1 > p2 (The proportion of Seldane users experiencing drowsiness is greater than that of placebo users)
We have the following sample data:
- Proportion of Seldane users reporting drowsiness: p1 = 9% of 800
- Proportion of placebo users reporting drowsiness: p2 = 8% of 650
At the 5% level of significance, we calculate the test statistic and corresponding p-value. If the calculated p-value is less than the significance level (0.05), we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
After performing the statistical test (which should be done through statistical software or formulas designed for comparison of two proportions), we will compare the p-value to the alpha (0.05). If the test statistic p-value is greater than 0.05, the decision is to fail to reject the null hypothesis H0. Otherwise, we would reject the claim.