## Question 860:

Problem # 1:
Clothing for Runners: Your company sells exercise clothing and equipment on the internet. To design the clothing, you collect a data on the physical characteristics of you different types of customers. Here are the weights in (in kilograms) for a sample of 24 male runners. Assume that the runners can be viewed as a random sample of your potential male customers. Suppose also that the standard deviation is known to be "σ = 4.5 kg."
68.7 61.8 63.2 53.1 62.3 59.7 55.4 58.9 60.9 69.2 63.7 67.8
65.6 65.5 56.0 57.8 66.0 62.9 53.6 65.0 55.8 60.4 69.3 62.1
Give a 95% confidence interval for , the mean of the population from which the sample is drawn. It is x bar +/ margin of error = 61.79 +/- ______
Problem #2:
The cost of health care is the subject of many studies that use statistical methods. One such study estimated that the average length of service for home health care among people over the age of 65 who use this type of service is 96.0 days with a standard error of 5.1 days. Assuming a very large sample, what is the 90% confidence interval for the mean length of service for all user of home health care. It is 96.0 +/- _____

Problem # 3:
Executive Learn Spanish: the table below gives the pretest and posttest scores on the MLA listening test in Spanish for 20 executives who received intensive training in Spanish.
Subject Pretest Posttest Subject Pretest Posttest
1 30 29 11 30 32
2 28 30 12 29 28
3 31 32 13 31 34
4 26 30 14 29 32
5 20 16 15 34 32
6 30 25 16 20 27
7 34 31 17 26 28
8 15 18 18 25 29
9 28 33 19 31 32
10 20 25 20 29 32

The summary statistics for the difference is
Mean 1.45
Standard Error 0.716259
Median 2
Mode 3
Standard Deviation 3.203206
Sample Variance 10.26053
Kurtosis -0.38739
Skewness -0.49821
Range 12
Minimum -5
Maximum 7
Sum 29
Count 20
Confidence Level(90.0%) 1.238506

Give a 90% confidence interval for the mean increase in listening score due to the intensive training. It is 1.45 +/- _____