II. On June 30, 2021 the sample mean gas price in Georgia is $2.91 with a standard deviation of $0.32, and the sample mean gas price in Florida is $3.00 with a standard deviation of $0.45. The sample means are based on 205 Georgia gas stations, and 290 Florida gas stations. Test for differences in mean gas price between Georgia and Florida. Is it worth it for someone right on the border in Florida to come to Georgia to buy gas? Assume the sample was randomly sampled. a. What assumptions must you make when performing a hypothesis test to compare two group means? (Four assumptions). And, what do these assumptions tell us (in other words, why make these assumptions)? b. Fill in the values for the following variables: Group 1 (Georgia) Group 2 (Florida) NI= X1 - S1 = S1= di = c. State your research and null hypotheses using a two-tailed test. (I can think of no obvious reason they we would hypothesize one would be lower higher, unless you know something I don't know) d Using a = 0.01 (a 99% confidence level) compute the test statistic using a t-distribution (as our population standard deviation is unknown). e. What can you conclude about your hypothesis (reject or fail to reject the null-base this on alpha or the critical value)" Is there a significant difference in the price of gasoline for Georgians and Floridians? Interpret your result in at least two sentences. Make sure to refer to the specific units of the variable, the specific population, the source, and your confidence level