Statistical analysis for undergraduate GPA

1. The undergraduate GPA for students admitted to the top graduate business schools was 3.37 Assume this estimate was based on a sample of 120 students admitted to the top schools. Using past years' data, the population standard deviation can be assumed known with Q=.28 What is the 95% confidence interval estimate of the mean undergraduate GPA for students admitted to the top graduate schools.

2. The first few weeks of 2004 were good for the stock market. A sample of 25 large open-end funds showed the following year-to-date returns through January 16, 2004.

7.0 3.2 1.4 5.4 8.5
2.5 2.5 1.9 5.4 1.6
1.0 2.1 8.5 4.3 6.2
1.5 1.2 2.7 3.8 2.0
1.2 2.6 4.0 2.6 0.6

a) What is the point estimate of the population ean year-tp-date return for large open-ended funds?
b) Given that the population has a normal distribution, develop a 95% confidence interval for the population mean year-to-date return for open-end funds.

3. America's young people are heavy Internet users: 87% of Americans ages 12 to 17 are Internet users. MySpace was voted the most popular website by 9% in a sample survey of Internet users in this age group. Suppose 1400 youths participated in the survey. What is the margin of error and what is the interval estimate of the population proportion for which MySpace is the most popular Website? Use a 95% confidence level.

4. Using the attached Excel file with data relating to 2500 managers of EAI, answer the following with this population data using Excel (show all formulas and actions in the final Excel file with answers; use separate sheets if necessary):
a) Find the mean and standard deviation (M and Q)
b) Assume that the population's normally distributed. Draw random 30 samples of size 2- each from this population using the mean and standard deviation that you obtained in question a) above. In Excel that we use, the number of variables is the same as the number of samples, and the number of random numbers is same as sample size. Find the mean and standard deviation of each sample using the function key of the Excel.
c) Compute 90% confidence interval for the population mean for each of the 30 random samples, assuming that the population standard deviation is unknown (use the sample standard deviation as an estimate of population standard deviation). Put "X" mark in the row next to the interval for those intervals that do not contain the population mean that you obtained in question1. Compute the percentage of the X marked intervals and reconcile with hte interpretation of 90% confidence level.

Note: In answering question c) compute the following for the very first sample:

- Find t by using the function key, use TINV function (probability in this case is 0.10 and d .f is19)
- Calculate the standard error as (s/Sq.Rte n)
- Find margin of error as (M.E) t* standard error (s/Sq.Rte n)
- Lower Confidence Limited (L.C.L)=sample mean - M.E
- Upper Confidence Limited (U.C.L)=sample mean + M.E
- Copy the formula to calculate each above item for the other 29 samples
- Finally, find the number of confidence intervals thath contain the population mean of 51,800 out of these 30 samples. In cases where the intervals don't contain 51,800 put an X mark in the cell below. As per theory, it should be 27 out of 30 giving you 90%