Final answer:
To test if 3% of users develop nausea from a drug, we perform a hypothesis test at the 0.01 significance level using the observed data of 165 cases of nausea out of 6015 patients. We calculate the test statistic or p-value to compare with the critical value. The result informs us whether nausea is a significant adverse reaction.
Step-by-step explanation:
Testing the Claim of Adverse Reaction Incidence
To test the claim that 3% of users develop nausea from the drug, we conduct a hypothesis test at the 0.01 significance level. We'll use the observed data where out of 6015 patients treated, 165 developed nausea. The null hypothesis (H0) states that the proportion of users who develop nausea is equal to 3% (0.03), while the alternative hypothesis (H1) states that the proportion is different from 3%.
The test statistic is calculated using the formula for a proportion z-test. Comparing the test statistic to the critical value or evaluating the p-value will determine if we should reject H0. If the p-value is less than the significance level, we reject H0, supporting the claim that the incidence of nausea is different from 3%.
Using the sample proportion (165/6015), we find the test statistic and compare it to the critical z-value for a 0.01 significance level. We may also use a statistical software or TI-83/84 calculator to find the p-value. If the p-value is less than 0.01, it suggests that nausea could be a more significant problem than initially claimed. However, if it is not lower, we do not have sufficient evidence to claim that the incidence of nausea is different from 3%.