The government would like to test the hypothesis that the average hourly wage for men is more than $2.00 higher than the average hourly wage for women. The following data summarizes the sample statistics for hourly wages for men and women. Assume that the population variances are unequal. Men Women Sample mean $25.40 $21.20 Sample size 10 11 Sample standard deviation $1.931 $4.5 If Population 1 is defined as men and Population 2 is defined as women, the degrees of freedom for this hypothesis test are ________.

Sony would like to test the hypothesis that the average age of a PlayStation user is lower than the average age of an Xbox user. A random sample of 32 PlayStation users had an average age of 33.7 years while a random sample of 36 Xbox users had an average age of 35.6 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.7 and 3.5 years, respectively. Sony would like to set α = 0.05. The critical value for this hypothesis test would be

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 32 PlayStation users had an average age of 33.7 years while a random sample of 36 Xbox users had an average age of 35.6 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.7 and 3.5 years, respectively. Sony would like to set α = 0.05. The p-value for this hypothesis test would be

Sony would like to test the hypothesis that the average age of a PlayStation user is lower than the average age of an Xbox user. A random sample of 32 PlayStation users had an average age of 33.7 years while a random sample of 36 Xbox users had an average age of 35.6 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.7 and 3.5 years, respectively. Sony would like to set α = 0.05. The p-value for this hypothesis test would be