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 $\alpha$.

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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.