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 17 Visa Gold cardholders resulted in a mean household income of $71,420 with a standard deviation of $9400 . A random survey of 9 9 MasterCard Gold cardholders resulted in a mean household income of $64,320 with a standard deviation of $9200. 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=0.05 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

Step 1:

Hypothesis:

Step 2:

Test statistic:

Degrees of Freedom:

Critical value:

   …………………..….using t table

Step 3:

Decision Rule:

Test statistic > Critical value, then Reject Ho at 5% level of significance.

Step 4:

Conclusion:

Test statistic < Critical value, 1.858 < 2.120, then Fail to Reject Ho at 5% level of significance.

Therefore, there is No difference in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold