Question

A) A person can take either of two routes to work, through Matteson or Richton Park. Both take on average 35 minutes, and travel times are Normally distributed. But are the variances of the travel times different? A random sample with n = 8 using the Matteson route, and another random sample with n = 6 using the Richton Park route, showed a variance of 45 (units: square minutes) and 30 respectively. To test whether the variances are different, the following test of hypothesis should be done: H0: sigma subscript 1 superscript 2 space equals space sigma subscript 2 superscript 2 H1: sigma subscript 1 superscript 2 space not equal to space sigma subscript 2 superscript 2 What is the value of the test statistic?

B) The current 401K plan at a work place is voluntary, and employees have to opt in. An HR manager believes that default enrollment of all employees in the 401K plan with an option to opt out leads to a higher participation rate. Let p1 be the population proportion of participation with the opt in plan (current) and let p2 be the population proportion of participation with the opt out plan (proposed). We have these hypotheses:

H0: p1 ≥ p2, H1: p1 < p2

Obviously, if H0 is right, we should stay with the current approach, but if we favor H1, we should enroll people by default.

What would be the implication of a type 2 error?

		we drop the enrollment of employees who are already on the 401K plan
		we force enrollment of employees who refuse to participate in the 401K plan
		we enforce the opt-out plan even though the current plan had higher participation
		we stay with the current plan, even though the new plan would have higher participation

Answer 1