A cell phone company offers two plans to its subscribers. At the time new subscr
ID: 3155508 • Letter: A
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 50 subscribers to Plan A is $46,600 with a standard deviation of $7,300. For a sample of 30 subscribers to Plan B, the mean income is $58,100 with a standard deviation of $6,300.
At the 0.05 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 value should be indicated by a minus sign. Round your answer to 2 decimal places.)
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u1 - u2 >= 0
Ha: u1 - u2 < 0
At level of significance = 0.05
As we can see, this is a left tailed test.
Calculating the means of each group,
X1 = 46600
X2 = 58100
Calculating the standard deviations of each group,
s1 = 7300
s2 = 6300
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 50
n2 = sample size of group 2 = 30
Thus, df = n1 + n2 - 2 = 78
Also, sD = 1545.574327
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = -7.440599782 [ANSWER, TEST STATISTIC]
**************************************************
Other details:
where uD = hypothesized difference = 0
Now, the critical value for t is
tcrit = - 1.664624645
Also, using p values,
p = 5.65464E-11
Comparing this to the significance level, WE REJECT THE NULL HYPOTHESIS.
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