To solve this problem, we will follow the steps of hypothesis testing for a proportion.

Part 1: Hypotheses

We want to test the claim that more than 20% of users develop nausea. The hypotheses are:

• Null hypothesis ($H_0$): $p = 0.20$
• Alternative hypothesis ($H_1$): $p > 0.20$

Thus, the correct answer is: D. $H_0$: $p = 0.20$, $H_1$: $p > 0.20$

Part 2: Test Statistic

The test statistic for a proportion is calculated using the formula: $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}$

Where:

• $\hat{p}$ is the sample proportion
• $p_0$ is the hypothesized population proportion
• $n$ is the sample size

Given:

• $\hat{p} = \frac{55}{215} \approx 0.2558$
• $p_0 = 0.20$
• $n = 215$

Let's calculate the test statistic:

$\hat{p} = \frac{55}{215} \approx 0.2558$ $z = \frac{0.2558 - 0.20}{\sqrt{\frac{0.20 \times 0.80}{215}}}$

First, compute the standard error:

$\text{Standard Error} = \sqrt{\frac{0.20 \times 0.80}{215}} \approx 0.0273$

Now, compute the $z$-value:

$z = \frac{0.2558 - 0.20}{0.0273} \approx 2.04$

Thus, the test statistic is: $z \approx 2.04$

Part 3: P-value

To find the p-value for a right-tailed test with $z = 2.04$:

Using standard normal distribution tables or a calculator:

$P(Z > 2.04) \approx 0.021$

Thus, the p-value is approximately: $0.021$

Part 4: Conclusion

We compare the p-value to the significance level $\alpha = 0.10$:

• If the p-value ≤ $\alpha$, reject $H_0$.
• If the p-value > $\alpha$, fail to reject $H_0$.

Since $0.021 < 0.10$, we reject $H_0$.

Thus, the correct conclusion is: D. Reject $H_0$. There is sufficient evidence to warrant support of the claim that more than 20% of users develop nausea.

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Do you want details or have any questions? Here are some more questions you can ask:

1. Can you explain the steps for hypothesis testing in more detail?
2. How do I interpret the p-value in hypothesis testing?
3. What are the common significance levels used in hypothesis testing?
4. Can you explain the difference between one-tailed and two-tailed tests?
5. How do I use a z-table to find the p-value for a test statistic?

Tip: When calculating the test statistic for a proportion, always double-check your sample size and sample proportion to ensure accuracy.