1. Reading achievement scores are obtained for a group of fourth graders. A score of 4.0 indicates a level of achievement appropriate for fourth grade, a score below 4.0 indicates underachievement, and a score above 4.0 indicates overachievement.

Assume that the population standard deviation equals 0.4. A random sample of 64 fourth graders reveals a mean achievement score of 3.82.

(a) Construct a 95 percent confidence interval for the unknown population mean. (Remember to convert the standard deviation to a standard error.)

(b) Interpret this confidence interval; that is, do you find any consistent evidence either of

Overachievement or of underachievement?

2.Imagine that one of the following 95 percent confidence intervals estimates the

Effect of vitamin C on IQ scores:

95% CONFIDENCE INTERVAL LOWER LIMIT UPPER LIMIT

1 100 102

2 95 99

3 102 106

4 90 111

5 91 98

(a) Which one most strongly supports the conclusion that vitamin C increases IQ scores?

(b) Which one implies the largest sample size?

(c) Which one most strongly supports the conclusion that vitamin C decreases IQ scores?

(d) Which one would most likely stimulate the investigator to conduct an additional experiment using larger sample sizes?