#### MS 150 Statistics Summer 2001 Test Two

1. The body fat percentage for the female students has a population mean of m of 31, a population standard deviation s of 8, and the data is normally distributed.
1. The highest acceptable body fat for young females is 31.  What percent of the female students have body fat lower than 31?  That is, find P(x<31).

2. The lower limit of obesity for young females is 39.  What percent of the female students have a body fat higher than 39?  That is, find P(x>39).

3. If there are 400 female students, how many are obese?

4. Suppose the College receives a grant to target the 80 most obese female students (equals the top 20%) with a diet and exercise program. What body fat should be set as the lower limit for entry into the program.  That is, find P(x > ?) = 0.20.

2. Saramen Chuuk Academy (SCA) has a sample mean TOEFL score of 470 with a population standard deviation s of 45 for n = 45 students.
1. Construct a 95% confidence interval for the population mean m for SCA.

2. Does the 95% confidence interval for SCA include the Berea Christian High School sample mean TOEFL score of 481?

3. Construct a 90% confidence interval for the population mean m body fat for male students using the following data:
10.5, 14.7, 16.4, 18.2, 19.8, 23.4, 25.7, 30.2, 32.5, 35.2, 45.9

Statistic Equations Excel
Square root =SQRT(number)
Sample size n =COUNT(data)
Sample mean =AVERAGE(data)
Population mean m
x P(x)
=AVERAGE(data)
Sample standard deviation sx
=STDEV(data)
Population standard deviation s
=STDEVP(data)
Slope =SLOPE(y data, x data)
Intercept =INTERCEPT(y data, x data)
Correlation =CORREL(y data, x data)
Find a probability p from a z value =NORMSDIST(z)
Find a z value from a probability p =NORMSINV(p)
Standard error of the population mean
Standard error of the sample mean
Determining the z-statistic zc from a =NORMSINV(1-a/2)
Error tolerance E of a mean for n ³ 30 using s =CONFIDENCE(a,s,n)
Error tolerance E of a mean for n ³ 30 using sx =CONFIDENCE(a,sx,n)
Error tolerance E of a mean for n < 30.  Can also be used for n ³ 30. [no Excel function, determine tc and then multiply by standard error of the mean as shown in the equation]
Determining tc from a and the degrees of freedom df. =TINV(a,df)
Calculate a confidence interval for a population mean m from a sample mean and an error tolerance E -E<m<+E