2022 has been a year marked by increasing inflation, particularly the rising cost of gasoline that spiked at the onset of the Russian invasion of Ukraine. For this project you will be considering the type of gasoline purchased and the cost per gallon. A simple random sample of 32 gasoline purchases was selected and the data appears in the table on the next page. For gas type, R represents Regular gas with an octane rating of 87, M represents Mid-Grade gas with an octane rating of 89, P represents Premium gas with an octane rating of 92, and D represents Diesel gas that is restricted to use in diesel engines. The cost per gallon is rounded to the nearest penny and the data recorded in dollars and cents.

1. This question uses the qualitative variable type of gasoline purchased.

(a). (10 points) Create a frequency table that lists the categories of the variable along with the frequency of occurrence of each category. Recall that there are four categories: Regular gas (R), Mid-Grade gas (M), Premium gas (P), and Diesel gas (D).

(b). (10 points) It is hypothesized that the proportion of all gas purchases that are Regular gasoline is 0.60, and of interest is to test this hypothesis versus the alternative hypothesis that the proportion of all gas purchases that are Regular gasoline is less than 0.60. Write out these two hypotheses in statistical notation.

(c). (10 points) List the assumptions required to test the hypotheses in part (b) and whether or not they are satisfied using the data collected.

(d). (15 points) Use the data in the table to test the hypotheses in part (b) at significance level = .10. Complete the test even if the assumptions are violated.

2. This question uses the quantitative variable cost per gallon of gasoline in dollars and cents.

(a). (10 points) Construct an appropriate stem-and-leaf plot to graphically display this data.

(b). (10 points) Calculate the mean, median, range, standard deviation, and interquartile range for this sample of data.

(c). (10 points) Use the results of parts (a) and (b) to completely describe the distribution of the data.

(d). (10 points) The goal is to calculate a confidence interval for the mean cost of all gallons of gasoline purchased. List the two assumptions that must be satisfied in order for the confidence interval to be computed, and whether or not they are satisfied using the data collected.

(e). (15 points) Calculate and interpret a 95% confidence interval for the mean cost of all gallons of gasoline purchased. Complete the calculation and interpretation even if the assumptions are violated.