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:

---

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).