Question

In: Statistics and Probability

Use these 30 numbers for part one 1.15, 1.15, 1.15, 1.15, 1.16, 1.29, 1.20, 1.26, 1.26,...

Use these 30 numbers for part one

1.15, 1.15, 1.15, 1.15, 1.16, 1.29, 1.20, 1.26, 1.26, 1.26, 1.28, 1.34, 1.39, 1.39, 1.45, 1.45, 1.49, 1.59, 1.59, 1.39, 1.35, 1.36, 1.38, 1.39, 1.49, 1.45, 1.46, 1.48, 1.48

the mean for part 2 is 1.55

the mean for part 3 is 1.90

Part 1 - Estimate the mean price of regular gasoline in the Dayton area by taking a sample.

What is the population you will be studying?
Think carefully about how you are going to get a good sample to calculate a sample mean and collect the sample. For example, driving around your neighborhood is an example of a convenience sample and should not be done. Think of a more efficient way to collect gas prices that will also cover the whole Dayton area. Write a paragraph or two explaining how you collected your sample and why you think your sample is representative of Dayton gas prices.
What is the sample mean?
Construct a 95% confidence interval for the population mean price of gasoline in the Dayton area.
Explain what this confidence interval tells you.

Part 2 - Compare your sample estimate to the current mean gas in the State of Ohio.

Find the mean price of gasoline in the State of Ohio. You might try this GasBuddy website.
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. Show your work.
Using a significance level of 0.05, what is your conclusion?

Part 3 - Compare your sample estimate to the current mean gas in the U.S.

What is the mean price of gasoline in the U.S.? You might try reading the graph on this GasBuddy website.
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. Show your work.
Using a significance level of 0.05, what is your conclusion?

You will need to show all your work, step-by-step, and write a final summary of the results

Expert Solution

Note : Allowed to solve only one question per post. Hence solved Part A in complete detail.

What is the population you will be studying?
The population is the gas station in Dayton area.

Inorder to make sure that there is no bais introduced in the study. We need to randomly select the gas stations.

Step 1 : Make a list of all the gas station in Dayton area.
Step 2 : Assign a number from 1 to whatever number of station we have in the area. Every gas station now is represented by one number.
Step 3 : Now random select 30 number out the total number of gases station.
Step 4 : we need to travel or call up the gas station and find the price of gas in the station.

In this manner we can ensure that the sample is representative of the population.

What is the sample mean?
1.3528

Construct a 95% confidence interval for the population mean price of gasoline in the Dayton area.
Explain what this confidence interval tells you.

95% confidence interval for the mean is (1.3025, 1.403)

With a 95% confidence we can say that the true population mean of the gasoline price lies with the interval of (1.3025, 1.403)

Detailed working given below

Mean and standard deviation

95% confidence interval.

orchestra answered 2 years ago

how would you use randomly generated numbers to find 30 random numbers from 1 to 500?

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