FORMAT INSTRUCTIONS

Each question requires the use of MINITAB to solve. Please submit your work as a WORD or similar document. You can prepare this by cutting and pasting the results generated in MINITAB to such a document. Then you can edit that file with any required explanations (such as for part b of each question).Then just print that file as your submission.

1. Consider the data in problem 2.38 on page 63. This data consists of the cost of electricity during July 2013 for a random sample of 50 one-bedroom apartments in the New York City area. It is included in the data file, UTILITY.

a) Using this data, construct a 95% confidence interval for the population mean cost of electricity for such apartments in July 2013.

b) Briefly explain the meaning of this interval.

c) What is the margin of error when estimating the population mean cost of electricity during 2013 for one-bedroom apartments in that large city?

d) Do you think that the results in a, b, and c, could also be applied to other large cities throughout the U. S.? In other words, do these results generalize to other cities? Explain why or why not.

2. The following data represent the total fat, in grams per serving, for a sample of 20 chicken sandwiches from fast-food chains. This data is also contained in a file posted on BLACKBOARD and named “CHICKEN”.
7 8 4 5 16 20 20 24 19 30
23 30 25 19 29 29 30 30 40 56

a) Construct a 90% confidence interval for the mean total fat for the population of chicken sandwiches from fast food restaurants.

b) Statistical theory (the Central Limit Theorem) indicates that the interval created in part a) may not be reliable if the population shape is highly skewed. Using the data in the sample of 20 sandwiches, determine if you think this shape is highly skewed. (HINT: Methods for doing so were discussed in chapters 2 and 3. Ultimately, this is a subjective decision and so you just need to state your opinion and attempt to justify it with appropriate statistical evidence).

To answer these questions using Minitab, follow these steps:

Question 1:

a) Open the UTILITY data file in Minitab.

b) Use the menu path "Stat > Basic Statistics > 1-Sample Z" to open the 1-Sample Z dialog box.

c) In the Variables field, select the variable "Cost" that represents the cost of electricity.

d) In the Options tab, select the "Confidence Level" checkbox and enter 95.

e) Click "OK". Minitab will generate the confidence interval for the mean cost of electricity for one-bedroom apartments in July 2013.

Capture and paste the results in a Word document.

b) Briefly explain the meaning of this interval.

In a Word document, explain that the confidence interval represents the range of values within which we can be 95% confident that the true population mean cost of electricity for one-bedroom apartments in July 2013 lies. It is an estimate that suggests the range of probable values for the mean cost.

c) Return to Minitab and use the following steps to find the margin of error:

- In the Minitab output, locate the "Confidence Interval" section and identify the lower and upper limits provided.

- Subtract the lower limit from the upper limit to calculate the width of the confidence interval.

- Divide this width by 2 to find the margin of error.

Capture and paste the results in the Word document.

d) In the Word document, explain that the obtained results cannot be directly generalized to other large cities throughout the U.S. The given results specifically relate to the random sample of one-bedroom apartments in the New York City area during July 2013. The populations and conditions in other cities may differ, so separate analyses are needed for accurate generalization.

Question 2:

a) Open the CHICKEN data file in Minitab.

b) Use the menu path "Stat > Basic Statistics > 1-Sample t" to open the 1-Sample t dialog box.

c) In the Variables field, select the variable "Total Fat" representing the total fat content of chicken sandwiches.

d) In the Options tab, select the "Confidence Level" checkbox and enter 90.

e) Click "OK". Minitab will generate the confidence interval for the mean total fat of chicken sandwiches from fast-food restaurants.

Capture and paste the results in the Word document.

b) To determine if the population shape is highly skewed:

- Calculate the skewness using the formula: skewness = (3 * mean - median) / standard deviation.

- If the absolute value of the skewness is greater than 1, the distribution can be considered highly skewed.

- State your opinion on the shape of the distribution based on the calculated skewness and provide appropriate statistical evidence.

Capture and paste the results in the Word document.

Remember to answer each sub-question clearly and provide all necessary explanations and calculations in the Word document.

To solve these questions, you will need to use MINITAB software to calculate the required statistics and confidence intervals.

**Question 1**

a) To construct a 95% confidence interval for the population mean cost of electricity for one-bedroom apartments in July 2013, you need to follow these steps:
- Open the MINITAB software.
- Import the data file "UTILITY" containing the cost of electricity data.
- Go to "Stat" menu and select "Basic Statistics" and then "1-Sample t..."
- In the "Variables" box, select the variable containing the cost of electricity data.
- Under "Options", choose "Confidence level" and enter 95.
- Click "OK" to generate the output, which will include the confidence interval for the mean cost of electricity.

b) To explain the meaning of the confidence interval, you need to interpret it in the context of the problem. A 95% confidence interval means that if we repeatedly take random samples and calculate the confidence intervals, approximately 95% of those intervals will contain the true population mean cost of electricity for one-bedroom apartments in July 2013. In simpler terms, we can be 95% confident that the true mean cost of electricity falls within the calculated interval.

c) The margin of error when estimating the population mean cost of electricity during 2013 for one-bedroom apartments in that large city can be calculated using the formula: margin of error = critical value * standard error. The critical value depends on the desired level of confidence, which in this case is 95%. The standard error can be calculated from the output generated in part a.

d) Whether the results from part a, b, and c can be applied to other large cities throughout the U.S. depends on whether the data used to calculate those results are representative of other cities. If the sample of one-bedroom apartments in the New York City area is representative of other cities, then the results could generalize. However, it is important to consider factors such as differences in cost of living, demographic characteristics, and electricity pricing structures that may vary across cities.

**Question 2**

a) To construct a 90% confidence interval for the mean total fat for the population of chicken sandwiches from fast food restaurants, you need to follow similar steps as in question 1a.
- Open the MINITAB software and import the data file "CHICKEN" containing the total fat data.
- Go to "Stat" menu and select "Basic Statistics" and then "1-Sample t..."
- Select the variable containing the total fat data and choose a confidence level of 90%.
- Click "OK" to generate the output, which will include the confidence interval for the mean total fat.

b) To determine if the population shape is highly skewed using the data from the sample of 20 chicken sandwiches, you can visually inspect a histogram or use statistical tests for skewness. In the chapter 2 and 3 of the textbook, methods for determining skewness are discussed. You can also refer to MINITAB's "Descriptive Statistics" output which provides skewness statistics. Based on these results and any other evidence you find, state your opinion on whether the shape is highly skewed and try to justify it using appropriate statistical evidence.