Sample satisfaction scores about the two retailers by the customers are shown below. In the report, 100 means the respondent is completely satisfied. Assume that a population standard deviation of 12 is a reasonable assumption for both retailers. Conduct the hypothesis test and report the p-value. At a .05 level of significance what is your conclusion? Include the solution process.
Retailer A Sample size = 25 Sample mean = 79
Retailer B sample size = 30 sample mean = 71

Now we can calculate the degrees of freedom given by:

And now we can calculate the p value using the altenative hypothesis:

For this case the p value is lower than the significance so then we have enough evidence to reject the null hypothesis and we can conclude that the true means are different

Step-by-step explanation:

We assume that the population deviation is the same for both cases

And the statistic is given by this formula:

Where t follows a t distribution with  degrees of freedom

The system of hypothesis on this case are:

Null hypothesis:

Alternative hypothesis:

The info given is:

represent the sample size for group A

represent the sample size for group B

represent the sample mean for the group A

represent the sample mean for the group B

And now we can calculate the statistic:

Now we can calculate the degrees of freedom given by:

And now we can calculate the p value using the altenative hypothesis:

For this case the p value is lower than the significance so then we have enough evidence to reject the null hypothesis and we can conclude that the true means are different

step-by-step explanation: