Chapter 8.3, Problem 34PB

Heights of seedlings Exercise 8.7 reported heights (in mm) of 55.5, 60.3, 60.6, 62.1, 65.5, and 69.2 for six seedlings fourteen days after germination.

1. a. Using the web app, software or a calculator, verify that the 95% confidence interval for the population mean is (57.3, 67.1).
2. b. Name two things you could do to get a narrower interval than the one in part a.
3. c. Construct a 99% confidence interval. Why is it wider than the 95% interval?
4. d. On what assumptions is the interval in part a based? Explain how important each assumption is.

8.7 Nutrient effect on growth rate Researchers are interested in the effect of a certain nutrient on the growth rate of plant seedlings. Using a hydroponics growth procedure that used water containing the nutrient, they planted six tomato plants and recorded the heights of each plant 14 days after germination. Those heights, measured in millimeters, were as follows: 55.5, 60.3, 60.6, 62.1, 65.5, 69.2.

1. a. Find a point estimate of the population mean height of this variety of seedling 14 days after germination.
2. b. A method that we’ll study in Section 8.3 provides a margin of error of 4.9 mm for a 95% confidence interval for the population mean height. Construct that interval.
3. c. Use this example to explain why a point estimate alone is usually insufficient for statistical inference.