Statistical Methods for Psychology

Exercises 107

Exercises

4.1 Suppose I told you that last night’s NHL hockey game resulted in a score of 26–13. You

would probably decide that I had misread the paper and was discussing something other

than a hockey score. In effect, you have just tested and rejected a null hypothesis.

a. What was the null hypothesis?

b. Outline the hypothesis-testing procedure that you have just applied.

4.2 For the past year I have spent about $4.00 a day for lunch, give or take a quarter or so.

a. Draw a rough sketch of this distribution of daily expenditures.

b. If, without looking at the bill, I paid for my lunch with a $5 bill and received $.75 in

change, should I worry that I was overcharged?

c. Explain the logic involved in your answer to part (b).

4.3 What would be a Type I error in Exercise 4.2?

4.4 What would be a Type II error in Exercise 4.2?

4.5 Using the example in Exercise 4.2, describe what we mean by the rejection region and the

critical value.

4.6 Why might I want to adopt a one-tailed test in Exercise 4.2, and which tail should I choose?

What would happen if I chose the wrong tail?

4.7 A recently admitted class of graduate students at a large state university has a mean Gradu-

ate Record Exam verbal score of 650 with a standard deviation of 50. (The scores are rea-

sonably normally distributed.) One student, whose mother just happens to be on the board

of trustees, was admitted with a GRE score of 490. Should the local newspaper editor, who

loves scandals, write a scathing editorial about favoritism?

4.8 Why is such a small standard deviation reasonable in Exercise 4.7?

4.9 Why might (or might not) the GRE scores be normally distributed for the restricted sample

(admitted students) in Exercise 4.7?

4.10 Imagine that you have just invented a statistical test called the Mode Test to test whether the

mode of a population is some value (e.g., 100). The statistic (M) is calculated as

Describe how you could obtain the sampling distribution of M. (Note: This is a purely ficti-

tious statistic as far as I am aware.)

4.11 In Exercise 4.10 what would we call Min the terminology of this chapter?

M=

Sample mode

Sample range

.

Key Terms

Sampling error (Introduction)

Hypothesis testing (4.1)

Sampling distributions (4.2)

Standard error (4.2)

Sampling distribution of the differences
between means (4.2)

Research hypothesis (4.3)

Null hypothesis (H 0 ) (4.3)

Alternative hypothesis (H 1 ) (4.4)

Sample statistics (4.5)

Test statistics (4.5)

Decision-making (4.6)

Rejection level (significance level) (4.6)

Rejection region (4.6)

Critical value (4.7)

Type I error (4.7)

a(alpha) (4.7)

Type II error (4.7)

b(beta) (4.7)

Power (4.7)

One-tailed test (directional test) (4.8)

Two-tailed test (nondirectional test) (4.8)

Conditional probabilities (4.9)

Effect size (4.11)