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.