BIOS 603

One Sample Inference

• Learning Objective 19

  7.39-7.41 (Assume the population s.d. = the given sample s.d.) Answer

• Learning Objective 20

  7.39-7.41, 7.61, 7.62 Answer

• Learning Objective 21

  Problems
  We wish to test the null hypothesis that a mean equals 100 against an alternative that it is greater than 100. We will estimate power based on the specific alternative that the mean equals 105. The population standard deviation equals 20. The sample size is 25.
  
  a. What part of the null distribution contains the rejection region?
  b. What is the z score for alpha = .05?
  c. Convert the z score to a score based on a mean of 100 and the appropriate standard error.
  d. What is the power of the test?
  
  2. Repeat problem 1 for n = 100.
  
  3. Repeat problem 1 for the alternative hypothesis that the mean equals 90. Answer

• Learning Objective 22

  1. Solve for the sample size required for the following combinations of type I error and power. Use the information given in problem one for objective 21.

            type I error   Power
                .05         .8
                .05         .9
                .01         .8
                .01         .9
  

  Answer

• Learning Objective 23

  7.22, 7.24, 7.25 Answer

• Learning Objective 24

  7.51, 7.59 Answer

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