Module 9 (Chapters 8 and 9) Assignment
Problem 1
Quality Ratings of Airports. The International Air Transport Association surveys business travelers to
develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a
simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating
for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.
Develop a 95% confidence interval estimate of the population mean rating for Miami.
The interval estimate for the population mean rating in Miami is (5.74, 6.93).
To calculate this interval estimate, you'll need to determine the sample size and the mean of the provided data, which consists of 50 business travelers. The mean can be obtained by averaging the ratings of these travelers. Subsequently, the standard deviation for the ratings should be calculated using either the Excel formula =STDEV or the formula √(∑(x−¯x) ( x − x ¯ ) 2 /n).
Given that the confidence coefficient is 0.95, as stated in the problem, the level of significance is 1 - 0.95. With this information, you can determine the margin of error. This margin of error is then added and subtracted from the standard deviation to establish the interval estimate.
http://tavana.us/rutgers/assignments/CH89-Assignment-Problem1-Data.xlsx
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Problem 2
Telemedicine. Health insurers are beginning to offer telemedicine services online that replace the
common office visit. Wellpoint provides a video service that allows subscribers to connect with a physician
online and receive prescribed treatments (Bloomberg Businessweek). Wellpoint claims that users of its
LiveHealth Online service saved a significant amount of money on a typical visit. The data shown below
($), for a sample of 20 online doctor visits, are consistent with the savings per visit reported by Wellpoint.
Assuming the population is roughly symmetric, construct a 95% confidence interval for the mean savings
for a televisit to the doctor as opposed to an office visit.
The interval estimate for the mean savings from a visit to the doctor is (60.54, 81.46).
To calculate the interval estimate, you begin by determining the sample size, which in this case is
20, and finding the average of the data.
The standard deviation for the savings should be calculated using either the Excel formula
=STDEV or the formula √(∑(x−¯x) ( x − x ¯ ) 2 /n).
The confidence coefficient is 0.95, as specified in the problem. The level of significance is
calculated as 1 minus the confidence coefficient. As this is a two-tailed test, you divide the level of
significance by 2.
To determine the margin of error, the degrees of freedom need to be calculated, which is derived
by subtracting 1 from the sample size. This value is then used to find the T-value for the problem.
In this particular case, the margin of error can be found by multiplying the T-value by the sum of
the standard deviation divided by the square root of the sample size. Finally, this margin of error
is added and subtracted from the standard deviation to establish the interval estimate.
http://tavana.us/rutgers/assignments/CH89-Assignment-Problem2-Data.xlsx
