Question

A cell phone company offers two plans to its subscribers. At the time new subscribers sign up, they are asked to provide some demographic information. The mean yearly income for a sample of 40 subscribers to Plan A is $50,600 with a standard deviation of $9,200. For a sample of 30 subscribers to Plan B, the mean income is $64,300 with a standard deviation of $7,100.

At the 0.050 significance level, is it reasonable to conclude the mean income of those selecting Plan B is larger? Assume unequal population standard deviations. Hint: For the calculations, assume the Plan A as the first sample.

a. What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

The decision rule is to reject H0 if t is less than ?

b. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Answer 1

The statistical software output for this problem is:

Two sample T summary hypothesis test: Vi : Mean of Population 1 2 : Mean of Population 2 1 - P2 : Difference between two means Ho : 11-42 = 0 HA: P1 - H20 (without pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DF T-Stat P-value P1 - 2 -13700 1948.4182 67.92757 -7.0313448 <0.0001

Hence,

a) Decision rule: Reject Ho if t is less than -1.668

b) Test statistic = -7.03