Chapter 8, Sampling Distributions and Hypothesis Testing Video Solutions, Fundamental Statistics for the Behavioral Sciences

Problem 1

Suppose I told you that last night's NHL hockey game resulted in a score of 26 to 13 . You would probably decide that I had misread the paper, because hockey games almost never have scores that high, 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.

Harsh Gadhiya

Numerade Educator

01:43

Problem 2

For the past year I have spent about $$\$ 4$$ 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 (b).

Sheryl Ezze

Numerade Educator

04:45

Problem 3

What would be a Type I error in Exercise 8.2?

Jeremiah Mbaria

Numerade Educator

04:45

Problem 4

What would be a Type II error in Exercise 8.2?

Jeremiah Mbaria

Numerade Educator

02:07

Problem 5

Using the example in Exercise 8.2, describe what we mean by the rejection region and the critical value.

Joshua Argo

Numerade Educator

01:09

Problem 6

Why might I want to adopt a one-tailed test in Exercise 8.2, and which tail should I choose? What would happen if I choose the wrong tail?

Harsh Gadhiya

Numerade Educator

04:18

Problem 7

Imagine that you have just invented a statistical test called the Mode Test to determine whether the mode of a population is some value (e.g., 100). The statistic $(M)$ is calculated as
$$
\mathrm{M}=\text { Sample mode/Sample range }
$$

Describe how you could obtain the sampling distribution of M. (Note: This is a purely fictitious statistic.)

Jon Southam

Numerade Educator

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Problem 8

In Exercise 8.7, what would we call $\mathrm{M}$ in the terminology of this chapter?

Victor Salazar

Numerade Educator

02:45

Problem 9

It is known that if people are asked to make an estimate of something, for example, "How tall is the University chapel?"' the average guess of a group of people is more accurate than an individual's guess. Vul and Pashler (2008) wondered if the same held for multiple guesses by the same person. They asked people to make guesses about known facts. For example, "What percentage of the world's airports are in the United States?" Three weeks later the researchers asked the same people the same questions and averaged each person's responses over the two sessions. They asked whether this average was more accurate than the first guess by itself.
(a) What are the null and alternative hypotheses?
(b) What would be a Type I and Type II error in this case?
(c) Would you be inclined to use a one-tailed or a two-tailed test in this case?

Jameson Kuper

Numerade Educator

01:17

Problem 10

Define "sampling error."

Bernabe Montoya

Numerade Educator

01:41

Problem 11

What is the difference between a "distribution" and a "sampling distribution"?

Bryan Meares

Numerade Educator

01:43

Problem 12

How would decreasing $\alpha$ affect the probabilities given in Table 8.1?

Gaurav Kalra

Numerade Educator

04:16

Problem 13

Magan, Dweck, and Gross (2008) asked participants to choose, for example, between $$\$ 5$$ today or $$\$ 7$$ next week. In one condition, the choices were phrased exactly that way. In a second condition, they were phrased as " $$\$ 5$$ today and $$\$ 0$$ next week or $$\$ 0$$ today and $$\$ 7$$ next week," which is actually the same thing. Each person's score was the number of choices in which the smaller but sooner choice was made. The mean for the first group was 9.24 and the mean for the second group was 6.10 .
(a) What are the null and alternative hypotheses?
(b) What statistics would you compare to answer the question? (You do not yet know how to make that comparison.)
(c) If the difference is significant with a two-tailed test, what would you conclude?

Sheryl Ezze

Numerade Educator

06:11

Problem 14

For the distribution in Figure 8.51 said that the probability of a Type II error $(\beta)$ is . 64 . Show how this probability was obtained.

Neel Faucher

Numerade Educator

01:34

Problem 15

Rerun the calculations in Exercise 8.14 for $\alpha=.01$.

Sheryl Ezze

Numerade Educator

Problem 16

In the example in Section 8.10 , what would we have done differently if we had chosen to run a two-tailed test?

Check back soon!

03:00

Problem 17

Describe the steps you would go through to flesh out the example given in this chapter about the course evaluations. In other words, how might you go about determining if there truly is a relationship between grades and course evaluations?

Jameson Kuper

Numerade Educator

01:18

Problem 18

Describe the steps you would go through to test the hypothesis that people are more likely to keep watching a movie if they have already invested money to obtain the movie.

Sheryl Ezze

Numerade Educator

Problem 19

In the exercises in Chapter 2, we discussed a study of allowances in fourth-grade children. We considered that study again in Chapter 4, where you generated data that might have been found in such a study.
(a) Consider how you would go about testing the research hypothesis that boys receive more allowance than girls. What would be the null hypothesis?
(b) Would you use a one-tailed or a two-tailed test?
(c) What results might lead you to reject the null hypothesis, and what might lead you to retain it?
(d) What might you do to make this study more convincing?

Check back soon!

02:16

Problem 20

Simon and Bruce (1991), in demonstrating a different approach to statistics called "resampling statistics," ${ }^5$ tested the null hypothesis that the price of liquor (in 1961) for the 16 "monopoly" states, where the state owned the liquor stores, was different from the mean price in the 26 "private" states, where liquor stores were privately owned. (The means were $$\$ 4.35$$ and $$\$ 4.84$$, respectively, giving you some hint at the effects of inflation.) For technical reasons, several states don't conform to this scheme and could not be analyzed.
(a) What is the null hypothesis that we are actually testing?
(b) What label would you apply to $$\$ 4.35$$ and $$\$ 4.84$$ ?
(c) If these are the only states that qualify for our consideration, why are we testing a null hypothesis in the first place?
(d) Identify a situation in which it does make sense to test a null hypothesis here.

Nick Johnson

Numerade Educator

07:00

Problem 21

Several times in this chapter I have drawn a parallel between hypothesis testing and our judicial system. How would you describe the workings of our judicial system in terms of Type I and Type II errors and in terms of power?

Jeremiah Mbaria

Numerade Educator