Casey Fitch is writing a reportfora statistics class. He is investigating whether the population mean price for a gallon of regular gasoline at stations of Brand A are currently higher than the population mean price for a gallon of regular gasoline at stations of Brand B in the region. Casey randomly selects 34 service stations of Brand A and 35 service stations of Brand B and records the price for a gallon of regular gasoline. The sample mean price for Brand A is $2.836 with a sample standard deviation of $0.083, while Brand B has a sample mean price of $2.798 with a sample standard deviation of $0.049. Let 1 be the population mean price for a gallon of regular gasoline of Brand A and 2 be the population mean price for a gallon of regular gasoline ofBrand B. Casey usesthe alternative hypothesis Ha:12>0, with =0.05.He assumesthat the population standard deviations of the two groups are not equal, so he uses33 degrees of freedom. If the t-test statistic is t2.31 and the rejection region is greater than t0.05=1.692, what conclusion could be made about the population mean price of a gallon of regular gasoline ofBrand A and Brand B?Identify all of the appropriate conclusions.

Select all that apply:

Reject the null hypothesis.

Fail to reject the null hypothesis.

There is sufficient evidence at the =0.05 level of significance to conclude that the population mean price of a gallon of regular gasoline of Brand A stations is greater than the population mean price of a gallon of regular gasoline of Brand B stations.

There is insufficient evidence at the =0.05 level of significance to conclude that the population mean price of a gallon of regular gasoline of Brand A stations is greater than the population mean price of a gallon of regular gasoline of Brand B stations.