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Statistics 5371 Final Exam Review Fall 2012.

1. Suppose a researcher wants to design a new study with a power of 0.8 and a significance of 0.05 to test whether the caffeine content for a brand of coffee is really 100mg. A previous study gave a mean caffeine level for this brand of 110 mg and a standard deviation of 7 mg. Use PROC POWER to determine how many cups of coffee need testing.

2. A company did a study to estimate the effect of different promotional strategies on the market share of one of their products. Over a period of 36 months they varied their promotional strategy. There are four strategies: Ordinary (standard pricing and advertising); Discount (price discount with standard advertising); Promotion (standard pricing, …show more content…

c. Perform a one-factor analysis of variance for the data. Write the table below and interpret the result.

d. Regardless of the significance of your ANOVA, apply contrast defined by applying the weights (-0.5, 0.5, -0.5, 0.5) to the strategies (in the order listed). Calculate a 95% confidence interval for the contrast.

e. What does this contrast measure?

f. Interpret the confidence interval.

g. Suppose we believe that the effect of a price discount may depend on whether there is enhanced advertising or not. Develop a set of contrast weights that would measure the degree to which the effect of a price discount differs between the standard advertising and enhanced advertising settings.

3. The distribution of undergraduate grade point averages at a large university is approximately normal with a mean of 2.8 and a standard deviation of 0.4.

a. What proportion of GPAs is between 3.0 and 3.5?

b. The Dean of Students wants to place students with GPAs in the bottom 10% of the distribution on probation. What is the GPA cutoff for being placed on probation?

c. The designation of “summa cum laude” (roughly translated as “super high honors”) is reserved for the students with GPAs in the top 1% of all students. What is the GPA cutoff for “summa cum laude”?

d. The normal distribution may be a useful approximation, but it can’t exactly be the correct distribution. Explain why this is so.

e. What percentage of

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