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 12 visa gold cardholders resulted in a mean household income of $73,540 with a standard deviation of $9500. a random survey of 8 mastercard gold cardholders resulted in a mean household income of $63,360 with a standard deviation of $8500. is there enough evidence to support the executives claim? let $mu_1$ be the true mean household income for visa gold cardholders and $mu_2$ be the true mean household income for mastercard gold cardholders. use a significance level of $alpha = 0.05$ 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. answer 1 point $h_0:mu_1$ drop - down options: =, $
eq$, >, <, $geq$, $leq$ $mu_2$ $h_a:mu_1$ drop - down options: =, $
eq$, >, <, $geq$, $leq$ $mu_2$

Explanation:

Step1: Define null hypothesis

The null hypothesis ($H_0$) is a statement of no - difference. Here, it is that the mean household incomes for Visa Gold and MasterCard Gold cardholders are equal. So, $H_0:\mu_1=\mu_2$.

Step2: Define alternative hypothesis

The alternative hypothesis ($H_a$) is what the advertising executive claims. Since the claim is that there is a difference (not specifying greater or less), it is a two - tailed test. So, $H_a:\mu_1
eq\mu_2$.

Answer:

$H_0:\mu_1 = \mu_2$, $H_a:\mu_1
eq\mu_2$