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 solve these questions using MINITAB, follow these steps:
1. Open the MINITAB software.
2. Import the data files "UTILITY" and "CHICKEN" into MINITAB.
3. Perform the necessary calculations to answer each question.
Question 1:
a) To construct a 95% confidence interval for the population mean cost of electricity, use the data in the "UTILITY" file. Calculate the confidence interval as follows:
- Go to "Stat" > "Basic Statistics" > "1-Sample t".
- Select the variable containing the cost of electricity data.
- In the "Options" tab, choose the desired confidence level (95%).
- Click "OK" to generate the results.
Copy and paste the output into a WORD or similar document and label it as the answer to part a.
b) To explain the meaning of the confidence interval, you can write a brief explanation in your own words. Mention that the confidence interval provides a range of values within which we are 95% confident the true population mean cost of electricity lies. It represents the uncertainty associated with estimating the true population mean based on a sample.
Include this explanation in the WORD document after pasting the results.
c) The margin of error can be calculated using the formula:
Margin of Error = Critical Value * Standard Error
Where the critical value is based on the confidence level and the standard error is calculated based on the sample standard deviation and sample size.
- Look for the standard deviation and sample size in the output obtained in part a.
- Determine the critical value corresponding to the chosen confidence level (95%).
- Calculate the margin of error using the given formula.
Add these calculations to the WORD document after explaining part b.
d) To determine if the results in parts a, b, and c can be applied to other large cities throughout the U.S., you need to consider the concept of generalizability. Here, you can provide your opinion and rationale based on statistical reasoning.
- Mention that the results may not necessarily generalize to other cities due to potential differences in various factors such as demographics, electricity rates, and housing characteristics.
- Explain that while the data provides insights into the cost of electricity for one-bedroom apartments in the New York City area, it may not accurately represent other cities.
- Elaborate on the need for a representative and diverse sample from various cities to draw reliable conclusions for the entire U.S.
Add this explanation to the WORD document after addressing part c.
Question 2:
a) To construct a 90% confidence interval for the mean total fat of chicken sandwiches, use the data in the "CHICKEN" file. Calculate the confidence interval as follows:
- Go to "Stat" > "Basic Statistics" > "1-Sample t".
- Select the variable containing the total fat data.
- In the "Options" tab, choose the desired confidence level (90%).
- Click "OK" to generate the results.
Copy and paste the output into a WORD or similar document and label it as the answer to part a.
b) To determine if the population shape is highly skewed based on the sample data, you can use visual inspection and statistical tests.
- Create a histogram or boxplot of the data using MINITAB to visualize the distribution.
- Evaluate the shape based on visual cues such as symmetry or skewness.
- If necessary, perform a formal test for skewness using MINITAB's "Stat" > "Basic Statistics" > "Descriptive Statistics" option, selecting the variable for total fat. Look for the skewness value in the output.
Based on the results and your subjective judgment, state your opinion as to whether you think the shape is highly skewed. Justify your opinion using appropriate statistical evidence. Include this explanation in the WORD document after pasting the results for part b.
By following these steps, you can solve each question using MINITAB and provide explanations for each part.