Sony would like to test the hypothesis that the average age of a PlayStation user is different from the average age of an Xbox user. A random sample of 36 PlayStation users had an average age of 34.2 years while a random sample of 30 Xbox users had an average age of 32.7 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.9 and 4.0 years, respectively. Sony would like to set α = 0.10. The p- value for this hypothesis test would Be ______ .

Question

Quizplus · Accepted Answer

Given the sample sizes, means, and population standard deviations for both groups, and the significance level (α = 0.10), the correct p-value can be calculated using the formula for the two-sample z-test for the difference in means. The calculation involves determining the z-score first and then finding the corresponding p-value. The provided options suggest that the calculation has already been done, and among the options, A) 0.1260 is identified as the correct p-value for this hypothesis test. This p-value indicates the probability of observing a difference as large or larger than the one observed between the two sample means, under the assumption that there is no actual difference in the average ages of PlayStation and Xbox users. Since the p-value (0.1260) is greater than the significance level (α = 0.10), we fail to reject the null hypothesis, suggesting that there is not enough evidence to conclude a difference in the average ages between the two groups at the 10% significance level.

Sony Would Like to Test the Hypothesis That the Average