An advertising executive claims that the mean household income for credit card holders of Visa Gold is less than that of MasterCard Gold. The results of a random survey of 100 customers from each group are shown below. Do the results support the executive's claim? Use
alphaα
= 0.05.
|
Visa Gold - Sample 1 |
MasterCard Gold - Sample 2 |
|
x overbar 1x1 = $60,900 |
x overbar 2x2 = $64,300 |
|
s 1s1 = $12,000 |
s 2s2 = $15,000 |
|
n 1n1 = 100 |
n 2n2 = 100 |
Hypotheses
What are the null and alternative hypothesis?
(Enter the symbol only, ue the tool pallette for symbols.)
nothing11
=
nothing22
nothing11
nothing
nothing22
Calculate the Test Statistic and P-value.
Test Statistic
nothing
= nothing
P-value p = nothing
Test result
P-value
nothing
alphaα
A.Reject
Upper H 0H0.
B.Do not reject
Upper H 0H0.
Choose the correct conclusion below, with respect to the claim.
A.
There's not enough evidence to suggest the mean income of the Visa Gold cardmembers is less than the mean income of the MasterCard Gold cardmembers.
B.
There's enough evidence to suggest the mean income of the Visa Gold cardmembers is less than the mean income of the MasterCard Gold cardmembers.
C.
There's not enough evidence to reject the claim that the mean income of the Visa Gold cardmembers and the mean income of the MasterCard Gold cardmembers are the same.
D.
There's enough evidence to reject the claim that the mean income of the Visa Gold cardmembers and the mean income of the MasterCard Gold cardmembers are the same.
Click to select your answer(s).
| null hypothesis: Ho:μ1 =μ2 | ||
| Alternate hypothesis: Ha:μ1 <μ2 |
since sample size is large we use standard normal distriution (t distribution)
| Visa Gold | master Gold | |||
| sample mean x = | 60900.00 | 64300.00 | ||
| std deviation σ= | 12000.000 | 15000.000 | ||
| sample size n= | 100 | 100 | ||
| std error σx1-x2=√(σ21/n1+σ22/n2) = | 1920.937 | |||
| test stat z =(x1-x2-Δo)/σx1-x2 = | -1.77 | |||
| p value : = | 0.0384 | (from excel:1*normsdist(-1.77) | ||
since p value <0.05
option B is correct
There's enough evidence to suggest the mean income of the Visa Gold card members is less than the mean income of the MasterCard Gold card members.
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