Suppose we used StatCrunch to find the exact test statistic for a two-tailed (not equal to) hypothesis test for the mean, and it turned out to be 1.33. The population standard deviation is known. What is the p-value? 1836 None of the other choices are correct. 4082 0918
The Correct Answer and Explanation is:
To calculate the p-value for a two-tailed hypothesis test, we need to use the test statistic and compare it to the standard normal distribution. The test statistic in this case is given as 1.33.
Steps to Find the p-value:
- Determine the Z-Score:
The test statistic is already given as 1.33, which is the Z-score for this hypothesis test. The Z-score represents how many standard deviations the sample mean is away from the population mean. - Look Up the Z-Score:
To find the p-value associated with a Z-score of 1.33, we can use a Z-table or statistical software (like StatCrunch). A Z-table provides the cumulative probability for Z-scores. From a Z-table or calculator, the cumulative probability for a Z-score of 1.33 is approximately 0.9082. - Two-Tailed Test:
Since this is a two-tailed test, we are interested in both sides of the distribution (both the positive and negative tails). Therefore, we need to find the area in both tails of the normal distribution.- For a Z-score of 1.33, the area to the right of this Z-score is 1 – 0.9082 = 0.0918.
- Because it is a two-tailed test, we multiply the area by 2 to account for both sides of the distribution. Thus, the total p-value is: 2×0.0918=0.18362 \times 0.0918 = 0.18362×0.0918=0.1836
- Conclusion:
The p-value for a test statistic of 1.33 in a two-tailed test is 0.1836.
Interpretation:
- If the p-value is smaller than the significance level (typically 0.05), we would reject the null hypothesis.
- Since 0.1836 is greater than 0.05, we would fail to reject the null hypothesis, suggesting that there is not enough evidence to support the alternative hypothesis.
Thus, the correct p-value for this test is 0.1836, and the correct answer is 1836.
