Sony Would Like to Test the Hypothesis That the Average

Multiple Choice

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. Which one of the following statements is true?

A) Because the 90% confidence interval does not include zero, we fail to reject the null hypothesis and can conclude that the average age of PlayStation users is different from the average age of Xbox users.
B) Because the 90% confidence interval does not include zero, we reject the null hypothesis and can conclude that the average age of PlayStation users is different from the average age of Xbox users.
C) Because the 90% confidence interval includes zero, we fail to reject the null hypothesis and cannot conclude that the average age of PlayStation users is different from the average age of Xbox users.
D) Because the 90% confidence interval includes zero, we fail to reject the null hypothesis and conclude that the average age of PlayStation users is equal to the average age of Xbox users.