2022 has been a year marked by increasing inflation, particularly the rising cost of gasoline that spiked at the onset o

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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 𝞪 = .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.