Psychology 406 Assignment #5

1) Hays — Chapter 7, #8, #16, #20

2) Assume that Randy Researcher is doing his Master’s thesis and has developed a test of reading readiness for his experiment. He believes that the scores he gets from independent observations on children are N(μ, 4). In other words, he knows the variance but not the mean.

a) Randy wants to test the hypothesis H_{o}: μ = 5 versus H_{1}: μ = 8. If he has 9 independent observations (i.e., a random sample of 9 observations from the population of interest), what is the cutoff point for a significant result at α = .05 (α = .01)? What is the corresponding power for the test at α = .05 (α = .01)?

What would you say if he observed a sample mean of 4, or 5.5, or 7.5?

b) If Randy wishes to test H_{o}: μ ≤ 5 versus H_{1}: μ > 5, what is the cutoff value for the mean of 9 independent observations for α = .05 (α = .01)? What is the cutoff value’s relationship to your answer in (a)? Can you say anything about power?

c) Find the critical values (cutoff points) in a two-sided test of H_{o}: μ = 5 versus H_{1}: μ ≠ 5 (α = .01 and .05) for the sample of 9 observations. What is the relationship of the rejection region calculated here to the rejection region for the null hypothesis in (a)? Which of the two regions (i.e., calculated in (a) or (c)), would you prefer and when?

3) Suppose you flip a coin twenty times and get 18 heads. Would you reject the hypothesis that the coin is “fair”? Provide a p-value. (Hint: Set up a “null” hypotheses and an alternative — use the normal approximation to the Binomial. Should your test be one-tailed or two-tailed? Why?)