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A research psychologist interested in the association between memory and stress administers a memory test to a random sample of 50 college freshmen at 4-year universities. The test is purported to have a population standard deviation of 6.25. The test results of the sample yield a normal distribution and a sample mean of 78. Based on that information, answer the following questions:

1. Calculate the standard error (of the mean).
2. Calculate a 95% confidence interval to estimate of the mean score for the entire population of college freshmen at 4-year universities.
3. What does the confidence interval tell us about our "true" population mean (i.e., how do we interpret this estimate)?
4. What would happen to your interval width if you increased your confidence level to 99%? Why? (Calculations not required to answer this problem)

An ethologist is interested in determining the average weight of a new species found in the Galapagos Islands. Since it would be expensive and impractical to trap and measure the whole population, a random sample was taken. Here are the results: new species sample mean weight = 25 g, s = 6 g, n = 15

1. Determine the 95% confidence interval for the population mean weight of the species.
2. Keeping the mean and s the same, what would happen to your interval if n = 30? Why? (Calculations not required to answer this problem)

From a sample of 150 patients in a statewide drug rehabilitation program that you work for, you observe that 31% of patients were able to find employment within three months of entering the program.

1. Estimate the percentage of all patients in the statewide program who were able to find employment, using a 99% confidence interval.
2. What is the margin of error in this problem?
3. Your supervisor tells you that the margin of error is too high. What should you recommend?