H0:P = 0.047 H1: P >0.47 This hypothesis test is a left-tailed test. Compute the value of the test statistic

Let's walk through the hypothesis test details you've provided.

1. **Null Hypothesis (H₀)**: \( P = 0.47 \)
2. **Alternative Hypothesis (H₁)**: \( P > 0.47 \)
3. **Type of test**: It seems there is a mismatch in your description. You mentioned a "left-tailed test," but the alternative hypothesis \( P > 0.47 \) actually suggests a **right-tailed test**.

### Hypothesis Test Statistic
To compute the value of the test statistic, we use the following formula for a **z-test for proportions**:

\[
z = \frac{\hat{p} - P_0}{\sqrt{\frac{P_0(1 - P_0)}{n}}}
\]

Where:
- \( \hat{p} \) = sample proportion
- \( P_0 \) = population proportion under the null hypothesis (0.47)
- \( n \) = sample size

### What do we need?
- **Sample proportion \( \hat{p} \)**
- **Sample size \( n \)**

Once you provide those values, we can compute the test statistic \( z \).

Would you like to provide the sample data so we can calculate the test statistic? If not, here are some relevant follow-up questions:

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### 5 Related Questions:
1. What is the sample proportion \( \hat{p} \) in this scenario?
2. What is the sample size \( n \) for this hypothesis test?
3. Why is the test described as left-tailed when the alternative hypothesis suggests otherwise?
4. How do you interpret a right-tailed test in hypothesis testing?
5. What confidence level are you working with for this test (e.g., 95%)?

### Tip:
In hypothesis testing, always match the tail direction of the test (left, right, or two-tailed) with the inequality sign in the alternative hypothesis (e.g., > for right-tailed).

H0:P = 0.047 H1: P >0.47 This hypothesis test is a left-tailed test. Compute the value of the test statistic.

Learn how to compute the test statistic for a right-tailed z-test for proportions, with null hypothesis P = 0.47 and alternative hypothesis P > 0.47. Understand the key concepts in hypothesis testing, including how to apply the z-test formula and interpret the results. Suitable for college-level statistics students.

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