Assignment – Show the set up of each problem and the formula used when working these problems.
In a poll of 500 voters in a campaign to eliminate non-returnable beverage containers, 225 of the voters were opposed. Develop a 92% confidence interval estimate for the proportion of all the voters who opposed the container control bill.
A random sample of 94 contractors had an average yearly income of $97,000 with a standard deviation of $8,000.
- 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 was it calculated?
- Develop a 95% confidence interval for the average yearly income of all pilots.
In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 25 pieces of carry-on luggage was collected and weighed. The average weight was 14 pounds. Assume that we know the standard deviation of the population to be 7.5 pounds.
- Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage.
- Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.
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 11.8 to 12.2 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 1.45, determine the size of the sample.
For these project assignments throughout the course you will need to reference the data in the ROI Excel spreadheet. Download it here.
Hint from Dr. Klotz – use the information beginning in section 8.4 for #1
Using the ROI data set:
- For each of the 2 majors consider the â€˜School Typeâ€™ column. Assuming the requirements are met, construct a 90% confidence interval for the proportion of the schools that are â€˜Privateâ€™. 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.
- From the chart on page 340, what is your z-sub-alpha-over-two?
- Show how these values have been inputted into the formula and what the result was.
- Explain how to get the interval. What do you do with the answer from #6?
- 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 â€˜Annual % ROIâ€™. Be sure to interpret your results. Here’s some direction – this time, the data values are numbers rather than public/private. The formula has to be different because there is no “success/failure” option, but rather numbers.
- What is the mean of the data set?
- What is the standard deviation of the data set?
- What is your z-sub-alpha-over-two?
- What formula will you use, and why?
- Show your work as you calculate.
- What do you have to do with your answer in #5 to get the interval?
State and interpret the interval