This is the Confidence Interval Example 1 Problem Set for OMGT6123.  Please peruse the video tutorial of the solution posted to the course website. 

OMGT6123 Confidence Intervals I

1.       1.       Sue is given 225 data points.  The mean of the data set is 450 and the standard deviation of the sample is 50. 

          a.     Her boss asks her to estimate an interval that would contain 95% of the values for the data set.  Help Sue out. 

          b.     Someone said that if the variance of the data doubled that the confidence interval would double in size.  Is this true?  Show your work and process.

 2.      2.       Jackie is studying for her Quant Methods final and comes upon another interesting confidence interval problem.  The problem states that the standard deviation of a data set is 4975, a sample size of 73, and a certain percentage of values lie between 3000 and 6000.  However, her roommate again spilled coffee on the old exam and she cannot read what the percentage is.  Can you help her figure out what percentage of values lie between these two numbers (i.e., what is the confidence level)?

3.       3.       Doc knows that 95% of the average sales values for the month fall between $175k and $475k. 

          a.     However, he wishes to know what an estimate of the sample standard deviation would be if his sample size was 100.  Can you help him?

          b.     Doc finds out that the 95% measurement is incorrect.  The proper measurement is actually 99%.  What is the estimate of the sample standard deviation with this new information using the same sample size?

4.       4.        Kelly heard about a study on starting salaries of recent college graduates.  That study stated that on average recent college graduates make $44,000 with a sample standard deviation of $1,200 & a sample size of 225.  Kelly conducts her own study of 100 recent graduates that on average they started at $44,900 with a sample standard deviation of $2,500. 

          a.     Create a 99% confidence interval with the original study data.

          b.     She believes with 99% confidence that the graduates from her study on average make higher starting salaries.  Create a 99% C.I. for her data to help here explain her thoughts on this.

          c.     Assuming the numerical statistics given above stay the same, what would she conclude if her sample size were 49?  Assume 99% confidence.