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Week 5 Assignment

Hints: I am putting capital letters in the problems to help you align each of these problems with one of the formulas in this week’s Notations and Symbols.

Another hint from Dr. Klotz: Here are my favorite online z sub alpha over two calculator and t sub alpha over two calculator: Keep them handy.

http://simulation-math.com/_Statistics/FindZalphaover2.cshtml

http://simulation-math.com/_Statistics/Findtalphaover2.cshtml

Question 1

In a poll of 800 voters in a campaign to eliminate non-returnable beverage containers, 510 of the voters were opposed. Develop a 96% confidence interval estimate for the PROPORTION of all the voters who opposed the container control bill.

Question 2

A random SAMPLE of 25 airline pilots had an average yearly income of $99,000 with a SAMPLE STANDARD DEVIATION of $6,000.

  1. 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?
  2. 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 600 pieces of carry-on luggage was collected and weighed. The average weight was 28 pounds. Assume that we know the POPULATION standard deviation of the to be 4.3 pounds.

  1. Determine a 98% confidence interval estimate for the mean weight of the carry-on luggage.

Question 4

A statistician employed by a consumer testing organization reports that at 99% confidence he has determined that the true average content of the bottled Uncola soft drinks is between 15.90 to 16.10 ounces. He further reports that his sample revealed an average content of 16 ounces, but he forgot to report the size of the sample he had selected. Assuming the standard deviation of the population is 0.4, determine the size of the sample.

Project Week 5

For these project assignments throughout the course you will need to reference the data in the ROI Excel spreadheet. Download it here.

Using the ROI data set:

  1. For each of the 2 majors consider the ‘School Type’ column. Assuming the requirements are met, construct a 93% confidence interval for the PROPORTION of the schools in the SAMPLE that are ‘Private’. Be sure to interpret your results. We do not know the population standard deviation.
  2. For each of the 2 majors construct a 93% confidence interval for the MEAN of the column ‘Annual % ROI’. We do not know the population standard deviation.
  3. In a highlighted box, discuss the following. In Week 2, we could find the mean of the sample for ROI. We could say one was higher than the other. While that’s “nice,” it’s not enough. Now, instead of a single figure, we have a range called a confidence interval. How do these confidence intervals provide information about the which is the better major in terms of Annual ROI? Make sure you mention (see the discussion) why this week opened the doorway to something we have not been able to discuss before. THIS IS HUGE!!! Is a 93% confidence interval a guarantee that the ROI will be in the interval? Why or why not? Remember that written portions belong on a MS Word document.

Hints – these websites might help to find z or t sub alpha over 2. (you have to know which one)

http://simulation-math.com/_Statistics/FindZalphaover2.cshtml

http://simulation-math.com/_Statistics/Findtalphaover2.cshtml

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