Question Description

Please complete the following exercises. For any questions that require you to work out a problem, please show your work. Please note, you will not receive credit if you do not show your work on problem exercises. If you want to type it out, that is just fine. Alternatively, you can do it by hand, snap a photo, and paste into the document (just make sure it is clear). It is up to you.

As usual, this assignment is due by Sunday at 11:59 pm MST.

Exercise 1

Calculate the standard error of the mean for the following sample sizes:

  • 200
  • 500
  • 1000

Assume the standard deviation of the population is $23,000. Ensure that you show your work.

Exercise 2

A government program in a European country is set up to distribute subsidized business loans in towns with a mean independent, single-owned business income below 30,000 euros. Samples of 600 such business are taken from each town. If a town’s mean business income, based on its sample, is calculated as 30,500 euros, with a sample standard deviation of 7,000 euros, should it be disqualified from the program? Why or why not? Base your answer on 95% confidence intervals and ensure that you show your work.

Exercise 3

In the 2012 presidential election, much was made of the Republican candidate’s religion. W. Mitt Romney is a practicing member of the Church of Jesus Christ of Latter-Day Saints. In the 2012 ANES survey, individuals were able to rate parties, candidates, and groups on a 0-100 feel thermometer scale. Measuring their feelings toward members of the LDS church, we calculated:

  • A sample mean of 50.48 degrees
  • A sample standard deviation of 21.90 degrees
  • A sample size of 5,385

Using a 95% confidence interval, what is the range of estimates of the mean from which this sample was drawn. Assume random sampling and ensure that you show your work.