You are concerned that nausea may be a side effect of Tamiflu, but you cannot just give Tamiflu to patients with the flu and say that nausea is a side effect if people become nauseous. This is because nausea is common for people who have the flu. From past studies you know that about $30 \%$ of people who get the flu experience nausea. You collected data on 2203 patients who were taking Tamiflu to relieve symtoms of the flu, and found that 716 experienced nausea. Use a 0.01 significance level to test the claim that the percentage of people who take Tamiflu for the relief of flu symtoms and experience nausea is greater than $30 \%$.
a) Identify the null and alternative hypotheses?
b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)?
left-tailed
right-tailed
two-tailed
c) Identify the appropriate significance level.
\[
0.01 \checkmark 0^{\circ}
\]
d) Calculate your test statistic (use $\widehat{p}$ rounded to 4 decimal places). Round your test statistic to 4 decimal places.
e) Calculate your $p$-value and round to 4 decimal places.
Answer
The final answer is that the test statistic is approximately \(\boxed{2.5617}\) and the p-value is approximately \(\boxed{0.0052}\). Since the p-value is less than the significance level, we reject the null hypothesis. This means that we have sufficient evidence to support the claim that the percentage of people who take Tamiflu for the relief of flu symptoms and experience nausea is greater than 30%.
Step 1 ：Identify the null and alternative hypotheses. The null hypothesis is that the percentage of people who take Tamiflu for the relief of flu symptoms and experience nausea is equal to 30%. The alternative hypothesis is that the percentage is greater than 30%.
Step 2 ：The type of hypothesis test to conduct is a right-tailed test because we are testing if the percentage is greater than a certain value.
Step 3 ：The appropriate significance level for this test is 0.01.
Step 4 ：Calculate the test statistic. The sample size (n) is 2203, the number of successes in the sample (x) is 716, and the hypothesized population proportion (p0) is 0.30. The sample proportion (p_hat) is calculated as x / n, which is approximately 0.3250. The test statistic is then calculated as (p_hat - p0) / sqrt((p0 * (1 - p0)) / n), which is approximately 2.5617.
Step 5 ：Calculate the p-value. The p-value is calculated as 1 - the cumulative distribution function (CDF) of the test statistic, which is approximately 0.0052.
Step 6 ：Since the p-value is less than the significance level (0.0052 < 0.01), we reject the null hypothesis. This means that we have sufficient evidence to support the claim that the percentage of people who take Tamiflu for the relief of flu symptoms and experience nausea is greater than 30%.
Step 7 ：The final answer is that the test statistic is approximately \(\boxed{2.5617}\) and the p-value is approximately \(\boxed{0.0052}\). Since the p-value is less than the significance level, we reject the null hypothesis. This means that we have sufficient evidence to support the claim that the percentage of people who take Tamiflu for the relief of flu symptoms and experience nausea is greater than 30%.
