Consider a clinical test of the drug Tamiflu. In the past, it was known that the drug causes dizziness as a side effect in 5% of all of its users. In the clinical test, 16 out of 300 Tamiflu users experienced dizziness as a side effect. A consumer advocacy group claims that this sample data shows that the rate of incidence of dizziness among Tamiflu users is no longer 5%. We want to test this claim at the 0.02 level of significance using the traditional method. Given the value for the test statistic, as well as the critical values for this test for alpha =0.02 (calculated prior), What is your conclusion based on this method?

Question 5Answer

a.
Since the test statistic falls outside the critical region, we reject the null hypothesis


b.
Since the test statistic falls outside the critical region, we fail to reject the null hypothesis


c.
Since the test statistic falls in the critical region, we fail to reject the null hypothesis


d.
Since the test statistic falls in the critical region, we reject the null hypothesis

To determine the correct conclusion, let's outline the setup and reasoning involved in a hypothesis test for the proportion of dizziness side effects in Tamiflu users. 

### Hypothesis Setup
1. **Null Hypothesis** (\( H_0 \)): The proportion of Tamiflu users experiencing dizziness is 5% (\( p = 0.05 \)).
2. **Alternative Hypothesis** (\( H_1 \)): The proportion of Tamiflu users experiencing dizziness is not 5% (\( p \neq 0.05 \)).

This is a **two-tailed test** because we are testing whether the dizziness rate is different from 5% (not specifically higher or lower).

### Significance Level and Decision Rule
- **Significance Level** (\( \alpha \)): 0.02.
- With \( \alpha = 0.02 \), the critical values define the boundaries for the rejection region in a two-tailed test. Thus, if the test statistic falls in the critical region (beyond these critical values), we reject the null hypothesis. Otherwise, we fail to reject it.

### Conclusion Based on Test Statistic and Critical Region
From the options:
1. **Option (a)**: Reject \( H_0 \) if the test statistic falls outside the critical region. This is incorrect because the critical region is where we reject \( H_0 \).
2. **Option (b)**: Fail to reject \( H_0 \) if the test statistic is outside the critical region. This is correct.
3. **Option (c)**: Fail to reject \( H_0 \) if the test statistic falls in the critical region. This is incorrect because the critical region is where we would reject \( H_0 \).
4. **Option (d)**: Reject \( H_0 \) if the test statistic falls in the critical region. This is correct.

Therefore, the **correct answer** depends on whether the test statistic lies in the critical region.

Since the test statistic value and the critical values are given, here’s the conclusion based on each outcome:

1. **If the test statistic is in the critical region**, we select:
   - **Option (d): "Since the test statistic falls in the critical region, we reject the null hypothesis."**
  
2. **If the test statistic is not in the critical region**, we select:
   - **Option (b): "Since the test statistic falls outside the critical region, we fail to reject the null hypothesis."**

If you have specific values for the test statistic and critical values, let me know so I can finalize the conclusion based on that data. 

Would you like to go over further details?

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Here are 5 related questions to explore:

1. How do we calculate the test statistic for a hypothesis test on proportions?
2. What is the interpretation of failing to reject the null hypothesis in this context?
3. How does a two-tailed test differ from a one-tailed test in hypothesis testing?
4. How is the significance level (\( \alpha \)) chosen in clinical trials, and what are the common standards?
5. Why might a consumer advocacy group be interested in testing side effect rates?

**Tip:** Remember that a two-tailed test examines deviations on both sides of the hypothesized proportion, making it sensitive to any difference, whether higher or lower.

Consider a clinical test of the drug Tamiflu. In the past, it was known that the drug causes dizziness as a side effect in 5% of all of its users. In the clinical test, 16 out of 300 Tamiflu users experienced dizziness as a side effect. A consumer advocacy group claims that this sample data shows that the rate of incidence of dizziness among Tamiflu users is no longer 5%. We want to test this claim at the 0.02 level of significance using the traditional method. Given the value for the test statistic, as well as the critical values for this test for alpha = 0.02 (calculated prior), what is your conclusion based on this method?

Analyze the results of a clinical test for Tamiflu to determine if the dizziness side effect rate is significantly different from 5%. This problem covers key statistical concepts such as hypothesis testing for proportions, two-tailed tests, and statistical significance at a 0.02 significance level. Suitable for college-level statistics students.

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