To compute the value of the test statistic for the given hypothesis test, we follow these steps:

1. State the hypotheses:

• Null hypothesis ($H_0$): $p = 0.11$
• Alternative hypothesis ($H_1$): $p > 0.11$ (this is a right-tailed test)

2. Formula for the Test Statistic (Z):

The test statistic for a proportion is given by the formula:

$Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}$

Where:

• $\hat{p}$ = sample proportion
• $p_0$ = population proportion under the null hypothesis (in this case, $p_0 = 0.11$)
• $n$ = sample size

3. Gather Information:

To proceed, I need:

• The sample proportion $\hat{p}$ (from the sample data)
• The sample size $n$

Once I have these values, I can compute the value of the test statistic $Z$.

Do you have the values for $\hat{p}$ and $n$? Feel free to provide them, and I can complete the calculation.

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Relative Questions:

1. What is the relationship between the sample proportion and population proportion in hypothesis testing?
2. How does the sample size impact the test statistic?
3. Why is this considered a right-tailed test, based on the alternative hypothesis?
4. What are the common significance levels used in hypothesis testing?
5. How can we interpret the result of the Z-test in terms of rejecting or failing to reject $H_0$?

Tip: When performing hypothesis testing, always check the assumptions (e.g., sample size and normality) before proceeding with the test.