Question

Estimate the mean price of regular gasoline in the Dayton area by taking a sample.

I have collected 30 gas prices in the Dayton area

2.70, 2.40, 2.58, 2.51, 2.54, 2.57, 2.50, 2.60, 2.65, 2.52, 2.30, 2.55, 2.30, 2.59, 2.54, 2.68, 2.78, 2.75, 2.71, 2.61, 2.70, 2.56, 2.58, 2.60, 2.62, 2.69, 2.55, 2.40, 2.34, 2.56

- What is the population you will be studying?
- What is the population parameter that you are wanting to measure?
- What is the sample mean?
- Construct a 95% confidence interval for the population mean price of gasoline in the Dayton area, assuming the population standard deviation is $0.075.
- Explain what this confidence interval tells you.

Part 2

- Find the mean price of gasoline in the State of Ohio.
- Set up a null and alternative hypothesis to see if your sample for Dayton is enough to prove that the population mean gasoline price in Dayton is different than the mean price in Ohio. Test the hypotheses, assuming the population standard deviation is $0.075. Show your work.
- Using a significance level of 0.05, what is your conclusion?

Part 3

- What is the mean price of gasoline in the U.S.?
- Set up a null and alternative hypothesis to see if your sample for Dayton is enough to prove that the population mean price in Dayton is different than the mean price in the U.S. Test the hypotheses, assuming the population standard deviation is $0.075. Show your work.
- Using a significance level of 0.05, what is your conclusion?

Answer #1

Part 1:

Population: price of regular gasoline in the Dayton area

Population parameter: Population mean price of regular gasoline in the Dayton

Sample mean=$2.566

95% confidence interval for the population mean price of gasoline in the Dayton area=

We are 95% confident that the true mean price of regular gasoline in the Dayton lies between $2.54 and $2.59.

Note: Part 2 and Part 3: Not possible to answer since price of gasoline in Ohio and US are not given.

Set up a null and alternative hypothesis and
test to see if your estimated mean price in Dayton is enough to
prove that the population mean gasoline price in Dayton is
different than the US mean price. Show your hand written
work using a test statistic/ rejection region
approach.
Find a p-value and explain what it tells you.
What is your conclusion? How does the mean price of regular
gasoline in Dayton compare to the national mean price?
Explain.
US...

The diameter of a brand of tennis balls is approximately
normally distributed, with a mean of 2.57 inches and a standard
deviation of 0.05 inch. A random sample of 10 tennis balls is
selected.
What is the probability that the sample mean is less than 2.56
inches?= 0.2643
What is the probability that the sample mean is between 2.55 and
2.58 inches?= 0.6319
The probability is 65% that the sample mean will be between what
two values symmetrically distributed around...

The average price of regular unleaded gasoline was reported to
be $2.34 in 2006. Use the price as the population mean and assume
the population standard deviation is $0.20. What sample size would
be needed to ensure a probability of 0.95 that the sample mean is
within $0.03 of the population mean? Please specify your answer to
the nearest whole number. If you answer is 120.73, please input 121
for your answer.
_____________
The Grocery Manufacturers of America reported that...

The regular gas price regular gas in the Lansing area is a
normally distributed random variable with a mean of $2.35 and a
coefficient of variation of 5%. What is the standard deviation?
What is the probability that the price of gas will be between $2.01
(lowest price in Lansing as of 2/11 –at 5200 S Pennsylvania Ave
& Simms Ct) and $2.30?

During a certain week (many years ago) the mean price of
gasoline in California was $2.024 per gallon with a standard
deviation of $0.053. A random sample of 47 gas stations was drawn
from this population. What is the probability that the mean price
of this sample was more than $2.042? Show your work.
Probability = nothing (round answer to four decimal
places)

3. A company that supplies gasoline nationwide reports that the
average price per gallon of regular gasoline is $ 8,150, with a
standard deviation of $ 428. There are 750 gasoline stations in the
country. Suppose a random sample from 40 gas stations is
selected.
b. What is the mean or expected value of the sample distribution
of the means?
c. What is the standard error of the sample distribution of the
means?
d. Write the syntax for the sample...

1.74, 1.74, 1.74, 1.84, 1.84, 1.85, 1.87, 1.87, 1.88, 1.88,
1.88, 1.89, 1.89, 1.89, 1.89, 2.25, 2.25, 2.25, 2.25, 2.25, 2.25,
2.19, 2.19, 2.19, 2.19
Find the sample mean and sample standard deviation.
Construct a 95% confidence interval for the population mean
price of gasoline in the Dayton area. Show all your hand
written work in doing this.
Explain what this confidence interval tells you.

The Energy Information Administration reported that the mean
retail price per gallon of regular grade gasoline was $3.56.
Suppose that the standard deviation was $.10 and that the retail
price per gallon has a bell-shaped distribution.
NOTE: Please use empirical rule approximations for this
problem.
a. What percentage of regular grade gasoline
sold between $3.46 and $3.66 per gallon (to 1 decimal)?
b. What percentage of regular grade gasoline
sold between $3.46 and $3.76 per gallon (to 1 decimal)?...

The Energy Information Administration reported that the mean
retail price per gallon of regular grade gasoline was
$3.49 . Suppose that the standard deviation was
$0.10 and that the retail price per gallon has a
bell-shaped distribution.
NOTE: Please use empirical rule approximations for this
problem.
a. What percentage of regular grade gasoline
sold between $3.29 and $3.59 per
gallon (to 1 decimal)?
95.0 %
b. What percentage of regular grade gasoline
sold between $3.29 and $3.59 per
gallon (to...

Bob Nale is the owner of Nale’s Quick Fill. Bob would like to
estimate the mean number of gallons of gasoline sold to his
customers. Assume the number of gallons sold follows the normal
distribution with a population standard deviation of 2.30 gallons.
From his records, he selects a random sample of 70 sales and finds
the mean number of gallons sold is 5.70.
What is the point estimate of the population mean? (Round your
answer to 2 decimal places.)...

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