Introductory Biostatistics

ments). Suppose that we know from using an in-person diet interview

method in an earlier large study that the standard deviation is 20. For-

mulate the null and alternative hypotheses if we want to test for any

di¤erences between the standard deviations of the two methods.

5.9 In Example 5.1 it was assumed that the national smoking rate among

men is 25%. A study is to be conducted for New England states using a

sample sizen¼100 and the decision rule

Ifpa 0 : 20 ;H 0 is rejected

whereH 0 is

H 0 :p¼ 0 : 25

wherepandpare population and sample proportions, respectively, for

New England states. Is this a one- or a two-tailed test?

5.10 In Example 5.1, with the rule

Ifpa 0 : 20 ;H 0 is rejected

it was found that the probabilities of type I and type II errors are

a¼ 0 : 123

b¼ 0 : 082

forHA:p¼ 0 :15. Findaandbif the rule is changed to

Ifpa 0 : 18 ;H 0 is rejected

How does this change a¤ectaandbvalues?

5.11 Answer the questions in Exercise 5.10 for the decision rule

Ifpa 0 : 22 ;H 0 is rejected

5.12 Recalculate thepvalue in Example 5.2 if it was found that 18 (instead of
15) men in a sample ofn¼100 are smokers.

5.13 Calculate the 95% confidence interval forpusing the sample in Exercise
5.12 and compare the findings to the testing results of Exercise 5.12.

5.14 Plasma glucose levels are used to determine the presence of diabetes.
Suppose that the mean log plasma glucose concentration (mg/dL) in
35- to 44-year-old is 4.86 with standard deviation 0.54. A study of 100

206 INTRODUCTION TO STATISTICAL TESTS OF SIGNIFICANCE