The test statistic of

zequals

1.83

is obtained when testing the claim that

pgreater than

0.3.

Find the​ P-value.

To find the P-value, let's walk through the process step by step, given that we have:

- The test statistic \( z = 1.83 \)
- We are testing the claim that \( p > 0.3 \), which is a **right-tailed test**.

### Step 1: Understand the context
For a **right-tailed test**, the P-value is the probability that the test statistic is greater than or equal to the observed value under the null hypothesis.

### Step 2: Use the z-distribution
We can find the P-value by looking at the standard normal distribution (z-distribution). The P-value is the area to the right of the z-score \( z = 1.83 \).

### Step 3: Look up or compute the P-value
From standard normal distribution tables, or by using a calculator, the cumulative probability (area to the left) for \( z = 1.83 \) is approximately 0.9664.

Since this is a right-tailed test, the P-value is:
\[
P(\text{P-value}) = 1 - P(Z \leq 1.83) = 1 - 0.9664 = 0.0336
\]

### Final Answer:
The P-value is approximately **0.0336**.

### Conclusion:
- If your significance level \( \alpha \) is 0.05, you would reject the null hypothesis because the P-value (0.0336) is less than \( \alpha \).

---

Would you like any further clarification on how this was computed?

### 5 Related Questions:
1. How does the P-value relate to the significance level in hypothesis testing?
2. What is the difference between a right-tailed and left-tailed test?
3. How do you interpret the result if the P-value is greater than the significance level?
4. What is the relationship between the test statistic and the P-value?
5. How can the normal distribution table be used for finding probabilities?

### Tip:
Always compare the P-value with the significance level \( \alpha \) to make a decision on the null hypothesis in hypothesis testing.

The test statistic of z equals 1.83 is obtained when testing the claim that p is greater than 0.3. Find the P-value.

Learn how to find the P-value when testing the claim that p is greater than 0.3, given a test statistic of z = 1.83. This detailed explanation covers hypothesis testing, right-tailed tests, and the use of the z-distribution. Ideal for college-level statistics students.

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