An advertising executive claims that there is a difference inthe mean household income for credit cardholders of Visa Gold andof MasterCard Gold. A random survey of 8 Visa Gold cardholdersresulted in a mean household income of $78,320 with a standarddeviation of $11,100. A random survey of 12 MasterCard Goldcardholders resulted in a mean household income of $68,070 with astandard deviation of $10,700. Is there enough evidence to supportthe executive's claim? Let μ1 be the true mean household income forVisa Gold cardholders and μ2 be the true mean household income forMasterCard Gold cardholders. Use a significance level ofα=0.05α=0.05 for the test. Assume that the population variances arenot equal and that the two populations are normallydistributed.
Step 1 of 4: State the null and alternative hypotheses for thetest.
Step 2 of 4: Compute the value of the t test statistic. Roundyour answer to three decimal places.
Step 3 of 4: Determine the decision rule for rejecting the nullhypothesis H0H0. Round your answer to three decimal places.
Step 4 of 4: State the test's conclusion.
....reject null hypothesis...fail to reject null hypothesis
