Suppose that the P-value in at wo tailed test is 0.0142. If it is known that the test statistics is negative, what is the P-value for the corresponding left tailed test?

In a two-tailed test, the P-value is the sum of the probabilities in both tails of the distribution. When we are given the P-value for a two-tailed test, it includes the probabilities for both the left and right tails.

Given:
- The P-value for the two-tailed test is \(0.0142\).
- The test statistic is negative, which implies that we are interested in the left tail for the left-tailed test.

For a two-tailed test:
\[ P_{\text{two-tailed}} = P_{\text{left tail}} + P_{\text{right tail}} \]

Since the two-tailed P-value is evenly split between the two tails:
\[ P_{\text{left tail}} = P_{\text{right tail}} = \frac{P_{\text{two-tailed}}}{2} \]

Therefore, for the left-tailed test:
\[ P_{\text{left tail}} = \frac{0.0142}{2} = 0.0071 \]

So, the P-value for the corresponding left-tailed test is \(0.0071\).

Would you like more details or have any questions? 

Here are 5 numbered questions for you to ask:
1. How do you interpret P-values in hypothesis testing?
2. Can you explain the difference between one-tailed and two-tailed tests?
3. What is the significance level in hypothesis testing?
4. How do you calculate the test statistic for a given dataset?
5. What are common misconceptions about P-values?

**Tip:** Remember that a smaller P-value indicates stronger evidence against the null hypothesis.

Explore how to interpret P-values in hypothesis testing using a left-tailed test example. Learn about the calculation involved when transitioning from a two-tailed test with a given P-value of 0.0142. Discover the significance of negative test statistics and their implication on hypothesis testing.

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