Question

An advertising executive claims that there is a difference in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold. A random survey of 1818 Visa Gold cardholders resulted in a mean household income of $⁢58,470 with a standard deviation of $⁢11,800. A random survey of 8 MasterCard Gold cardholders resulted in a mean household income of $⁢50,190 with a standard deviation of $⁢11,300. Is there enough evidence to support the executive's claim? Let μ1 be the true mean household income for Visa Gold cardholders and μ2 be the true mean household income for MasterCard Gold cardholders. Use a significance level of α=0.1 for the test. Assume that the population variances are not equal and that the two populations are normally distributed.

Step 1 of 4: State the null and alternative hypotheses for the test.

Step 2 of 4: Compute the value of the t test statistic. Round your answer to three decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0H0. Round your answer to three decimal places.

Step 4 of 4: State the test's conclusion.

Answer 1

To Test :-

H1 :-

H0 :-

Test Statistic :-


t = 1.701

Test Criteria :-
Reject null hypothesis if


DF = 14

t_{\alpha /2, DF} = t_{ 0.1 /2, 14 } = 1.761

Result :- Fail to Reject Null Hypothesis

Conclusion :- Accept Null Hypothesis

There is no sufficient evidence to support the claim that there is a difference in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold at 10% level of significance.