Question

Consider the following hypothesis test. H0: ≤ 12 Ha: > 12 A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.53. Compute a range for the p-value.

Answer 1

To compute the range for the p-value in the hypothesis test, we need to find the test statistic and determine the probability associated with the observed sample mean. Given the sample mean, sample standard deviation, and hypothesized mean, we can calculate the test statistic (Z-score) and find the probability using a Z-table. The range for the p-value in this case is (0.0138, 1).

Step-by-step explanation:

To compute the range for the p-value, we need to find the test statistic and use it to determine the probability associated with the observed sample mean.

Given that the sample mean x = 14, the sample standard deviation s = 4.53, and the hypothesized mean is μ ≤ 12, we can calculate the test statistic (Z-score) using

Z = (x - μ) / (s / √n) = (14 - 12) / (4.53 / √25) = 2 / (4.53 / 5) = 2 * (5 / 4.53) = 2.21 (approx.)

Now, we need to find the probability associated with the test statistic using a Z-table. Since the alternative hypothesis is Ha: > 12, we are interested in finding the probability of Z > 2.21. Looking up the Z-table, we find that the probability is approximately 0.0138.

Therefore, the range for the p-value is (0.0138, 1) since the p-value is the probability of observing a test statistic as extreme or more extreme than the one observed. The p-value falls within this range, indicating that it is greater than 0.0138.