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 $47,200 with a standard deviation of $9,200. For a sample of 30 subscribers to Plan B, the mean income is $51,500 with a standard deviation of $7,100. The population variances are not equal.

At the .01 significance level, is it reasonable to conclude the mean income of those selecting Plan B is larger? Hint: For the calculations, assume the Plan A as the first sample.

The test statistic is . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

The decision is (Click to select)do not rejectreject the null hypothesis that the mean of Plan B is larger.

The p-value is (Click to select)between 0.025 and 0.01between 0.01 and 0.05between 0.05 and 0.1 (Round your answer to 2 decimal places.)

Answer 1

n1= 40,  = 47200 , s1 = 9200

n2=30,  = 51500, s2= 7100.

Here, Plan A is the first sample.

H0:   

H1: <  

The population variances are not equal.

formula for test statistic

  

t = -2.2069

The test statistic is = -2.21

Now Calculate P-value using t- table we get

The p-value is = 0.015351 = 0.02

The p-value is = between 0.01 and 0.05

Decision Rule:

if P-Value    then reject Ho

if P-Value >   then failed to reject Ho

here  P-Value = 0.02 > 0.01 then failed to reject Ho

Hence,

The decision is do not reject the null hypothesis that the mean of Plan B is larger.