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Answer:
Null hypothesis:
Alternative hypothesis:
Comparing the p value with the significance level given we see that
so we can conclude that we can reject the null hypothesis, and a would be a significant difference between the in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold at 10% of significance .
Step-by-step explanation:
Data given and notation
represent the mean for Visa
represent the mean for the sample Mastercard
represent the population standard deviation for Visa
represent the population standard deviation for Mastercard
sample size for the group Visa
sample size for the group Mastercard
t would represent the statistic (variable of interest)
significance level provided
Develop the null and alternative hypotheses for this study?
We need to conduct a hypothesis in order to check if the means for the two groups are different, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:
(1)
t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Calculate the value of the test statistic for this hypothesis testing.
Since we have all the values we can replace in formula (1) like this:
What is the p-value for this hypothesis test?
First we need to calculate the degrees of freedom given by:
Since is a bilateral test the p value would be:
Based on the p-value, what is your conclusion?
Comparing the p value with the significance level given we see that
so we can conclude that we can reject the null hypothesis, and a would be a significant difference between the in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold at 10% of significance .