2022 has been a year marked by increasing inflation, particularly the rising cost of gasoline that spiked at the onset o
Posted: Wed May 11, 2022 6:03 am
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.
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.