Question 1
In a poll of 500 voters in a campaign to eliminate non-returnable beverage containers, 275 of the voters were opposed. Develop a 95% confidence interval estimate for the proportion of all the voters who opposed the container control bill.
Question 2
A random sample of 87 airline pilots had an average yearly income of $97,000 with a standard deviation of $3,000.
- If we want to determine a 95% confidence interval for the average yearly income, what is the value of t?
- What are the degrees of freedom for this problem, and how is this value calculated?
- Develop a 95% confidence interval for the average yearly income of all pilots.
Question 3
In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 100 pieces of carry-on luggage was collected and weighed. The average weight was 34 pounds. Assume that we know the standard deviation of the population to be 5 pounds.
- Determine a 90% confidence interval estimate for the mean weight of the carry-on luggage.
- What determined whether you used a t value or a z value?
Question 4
A statistician employed by a consumer testing organization reports that at 95% confidence he has determined that the true average content of the Uncola soft drinks is between 11.9 to 12.1 ounces. He further reports that his sample revealed an average content of 12 ounces, but he forgot to report the size of the sample he had selected. Assuming the standard deviation of the population is 0.5, determine the size of the sample.
Question 5
For these project assignments throughout the course you will need to reference the data in the ROI Excel spreadsheet. Download it here.
Using the ROI data set:
- For each of the 2 majors consider the ‘School Type’ column. Assuming the requirements are met, construct a 90% confidence interval for the proportion of the schools that are ‘Private’. Be sure to interpret your results.
- What are the two possible data values in this column?
- Given which data value you are looking for, which one is the “success?” Which one is the “failure?”
- What proportion of the values is the success? This is your p.
- How many values are there in all? This is your n.
- What is your z-sub-alpha-over-two value? Did you get it from the chart on page 340? I hope so…
- Show how these values have been put into a formula and what the result was.
- Explain how to get the interval. What did you do with your answer in the previous step?
- State and interpret the interval.
- Repeat these steps for the second major.
- For each of the 2 majors construct a 95% confidence interval for the mean of the column ‘Annual % ROI’. Be sure to interpret your results. This problem is different than the last one because of what is in column D. It’s numbers rather than public/private. For this reason, we can’t use the same formula because there is no “success proportion.”
- What is the mean of your data set?
- What is the standard deviation of your data set?
- How many numbers are in your data set?
- What is your z or t sub alpha over two?
- What formula will you use, and why?
- Show how you plugged your numbers into the formula and solved.
- What do you have to do with your answer to #6 to get the interval?
- State and interpret the interval.
In a highlighted box, make sure to summarize your findings from this week. What does this tell you about ROI?
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