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.