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 of12Visa Gold cardholders resulted in a mean household income of83,070with a standard deviation of10,400. A random survey of17MasterCard Gold cardholders resulted in a mean household income of76,200with a standard deviation of9700. Is there enough evidence to support the executive's claim? Let1be the true mean household income for Visa Gold cardholders and2be the true mean household income for MasterCard Gold cardholders. Use a significance level of=0.1for the test. Assume that the population variances are not equal and that the two populations are normally distributed.

• State the null and alternative hypotheses for the test.
• Compute the value of thettest statistic. Round your answer to three decimal places.
• Determine the decision rule for rejecting the null hypothesisH0. Round your answer to three decimal places.
• State the test's conclusion.