Question

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).

Answer 1

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.