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# Homework for Statistics Lesson 11

 `Answer Completely.` `Some calculations are required.` `Due Fri., July 29, 2005, 11:30:00.000, EDT.` `Due on the teacher's desk in BH114.`
1. (3 points) Using the 4:1 ratio of ß to alpha a one-tailed test, and alpha=0.01, find the minimum sample size which has the required power to discriminate between a mean of 110 and a mean of 115 when the population standard deviation is 15. Be sure to clarify the values of z which are summed.

2. (3 points) Repeat the question above with an effect size of 8. Is the n so small as to worry about using a t distribution as our sampling distribution instead of the normal distribution? If so, how would that complicate the process?

3. (2 points) Sketch the situation depicted in problem one above, including both sampling distributions (one centered on 110 and one centered on 115). Label the x axes in both units of IQ and z. Be sure to shade and label the alpha and ß regions.

4. (2 points) Find a sample size large enough to have a power of 0.80 when differentiating between a mean of 110 and mean of 112 with alpha=0.05, one tail, and a population standard deviation of 15.

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