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mathematics
statistics

Fundamental Statistics for the Behavioral Sciences 8th Edition David C. Howell - Solutions

As part of the Katz et al. (1990) study that examined test performance on a passage that a group of students had not read, the experimenters obtained the same kind of data from a smaller group of students who had read the passage (called the Passage group). Their data follow:Calculate the mode,
Create a sample of ten numbers that has a mean of 8.6. Notice carefully how you did this—it will help you later to understand the concept of degrees of freedom.
Calculate the measures of central tendency for the data on ADDSC and GPA in Appendix D—also available at this book’s website.
In Table 3.1 the reaction-time data are broken down separately according to whether we are looking at the same stimulus or whether the stimuli are mirror images of one another. The data can be found by going this book’s website and obtaining the data labeled as Tab3-1.dat. Using SPSS or similar
With reference to Exercise 4.13, if people take longer to process an image that has been both reversed and rotated, then the mean reaction time should depend on whether or not the comparison stimulus has been reversed. If reversal does not alter the difficulty of processing information, then the
In the exercises in Chapter 2 we considered the study by a fourth-grade girl who examined the average allowance of her classmates. Recall that 7 boys reported an average allowance of $3.18, while 11 girls reported an average allowance of $2.63. These data raise some interesting statistical issues.
In Chapter 3 (Figure 3.5) we saw data on grades of students who did and did not attend class regularly. What are the mean and median scores of those two groups of students? (The data are reproduced here for convenience.) What do they suggest about the value of attending class?
Seligman, Nolen-Hecksema, Thornton, and Thornton (1990) classified participants in their study (who were members of a university swim team) as Optimists or Pessimists. They then asked them to swim their best event, and in each case they reported times that were longer than the swimmer actually
In Exercise 4.22 women did not show much difference between Optimists and Pessimists. The first 17 scores in the Optimist group are for men and the first 13 scores in the Pessimist group are for men. What do you find for men?
Use LazStats or MYSTAT to examine the means and standard deviations in Exercise 4.22. (For LazStats use Descriptive/Breakdown. For MYSTAT use the two-sample t test under the hypothesis testing menu and skip over the material that you don’t know.)
If a student in Katz’s study simply responded at random (even without reading the questions), she would be expected to get 20 items correct. How does this compare to the measures we found in Section 4.5? Why should this not surprise you?
Plot the data for each of the three conditions in Table 4.2 and describe the results.
A group of 15 rats running a straight-alley maze required the following number of trials to perform to a predetermined criterion. The frequency distribution follows:Calculate the mean and median number of trials to criterion for this group. (You can either write out the 15 numbers or you can think
Given the following set of data, demonstrate that subtracting a constant (e.g., 5) from every score reduces all measures of central tendency by that amount.
Given the following data, show that multiplying each score by a constant multiplies all measures of central tendency by that constant.
Calculate the range, the variance, and the standard deviation for data that Katz et al. collected on SAT performance without reading the passage. The data follow:
Create two sets of scores with equal ranges but different variances.
Create a boxplot for the data in Exercise 5.1.In Exercise 5.1The data follow:
Create a boxplot for the data in Exercise 5.2.In Exercise 5.2.
Create a boxplot for the variable ADDSC in Appendix D. These data are available at https://www.uvm.edu/~dhowell/fundamentals8/DataFiles/Add.dat.
Using the data for ENGG in Appendix D perform the following: (a) Calculate the variance and the standard deviation for ENGG. (b) These measures should be greater than the corresponding measures on GPA. Can you explain why this should be? (We will come back to this later in Chapter 12, but see if
The mean of the data used in Exercise 5.1 is 46.57. Suppose that we had an additional subject who had a score of 46.57. Recalculate the variance for these data. (You can build on the intermediate steps used in Exercise 5.1.) What effect does this score have on the answers to Exercise 5.1?
Instead of adding a score equal to the mean (as in Exercise 5.15), add a score of 40 to the data used in Exercise 5.1. How does this score affect the answers to Exercise 5.1?
Use SPSS, or other software, to draw a set of boxplots (similar to Figure 5.4b) to illustrate the effect of increase the angle of rotation in the Mental Rotation dataset. The data can be found at https://www.uvm.edu/~dhowell/fundamentals8/DataFiles/MentalRotation.dat (A file with the “.sav”
Given the following data:(a) Draw a boxplot. (b) Calculate the standard deviation of these data and divide every score by the standard deviation. (c) Draw a boxplot for the data in (b). (d) Compare the two boxplots.
The following graph came from the JMP statistical package applied to the data in Table 5.3 on length of hospitalization. Notice the boxplot on the top of the figure. How does that boxplot compare with the ones we have been using?
Calculate the range, the variance, and the standard deviation for the data that Katz et al. collected on SAT performance after reading the passage.
In Section 5.10, statistics were computed from the reaction time data in Chapter 3. What would you conclude from these data about the relationship between accuracy and reaction time?
Everitt, as reported in Hand, Daly, Lunn, McConway, and Oserowski (1994), presented data on the amount of weight gained by 72 anorexic girls under one of three treatment conditions. The conditions were Cognitive Behavior Therapy, Family Therapy, and a Control group who received no treatment. The
Compare the mean, standard deviation, and variance for the data in Exercise 5.1 with their trimmed and Winsorized counterparts.The data in Exercise 5.1
Compare the mean, standard deviation, and variance for the data for the Cognitive Behavior condition in Exercise 5.21 with their 20% trimmed and Winsorized counterparts. Why is the Winsorized variance noticeably smaller than the usual variance?
Use LazStats or MYSTAT to reproduce the means, standard deviations, and other statistics in Exercise 5.19. (MYSTAT will give the most complete results. You will need to work out how to handle missing data, which are indicated with a period. The help menus will show you how to do this, and will good
Compare the answers to Exercises 5.1 and 5.2. Is the standard deviation for performance when people do not read the passage different from the standard deviation when people do read the passage?
In Exercise 5.1, what percentage of the scores fall within two standard deviations from the mean?
In Exercise 5.2, what percentage of the scores fall within two standard deviations from the mean?
Create a small data set of about seven scores and demonstrate that adding or subtracting a constant to each score does not change the standard deviation. What happens to the mean when a constant is added or subtracted?
Given the data you created in Exercise 5.6, show that multiplying or dividing by a constant multiplies or divides the standard deviation by that constant. How does this relate to what happens to the mean under similar circumstances?
Using what you have learned from Exercises 5.6 and 5.7, transform the following set of data to a new set with a standard deviation of 1.00.
Use the answers to Exercises 5.6 and 5.7 to modify the answer to Exercise 5.8 to have a mean of 0 and a standard deviation of 1.00.
Assuming that the following data represent a population of X values with μ 5 4 and s 5 1.58:(a) Plot the distribution as given.(b) Convert the distribution in (a) to a distribution of X − μ.(c) Go the next step and convert the distribution in (b) to a distribution of z.
A dean must distribute salary raises to her faculty for next year. She has decided that the mean raise is to be $2,000, the standard deviation of raises is to be $400, and the distribution is to be normal. She will attempt to distribute these raises on the basis of merit, meaning that people whose
We have sent out everyone in a large introductory course to check whether people use seat belts. Each student has been told to look at 100 cars and count the number of people wearing seat belts. The number found by any given student is considered that student’s score. The mean score for the class
Several years ago a friend of mine in the Communication Sciences department produced a diagnostic test of language problems that is still widely used. A score on her scale is obtained simply by counting the number of language constructions (e.g., plural, negative, passive) that the child produces
Unfortunately, the whole world is not built on the principle of a normal distribution. In the preceding exercise the real distribution is badly skewed because most children do not have language problems, and therefore produce all constructions correctly. (a) Diagram how this distribution might
We have referred several times to data on reaction times in a mental rotation task. These data can be found on this book’s website as Ex6–14.dat. Using SPSS, or a similar program, read in the data and plot a histogram of reaction times in seconds. Click on the appropriate box to superimpose a
In Exercise 6.14, what score would be equal to or greater than 75% of the reaction times if this distribution were normal. What score actually has 75% of the observations below it?
The data in Appendix D (available at www.uvm.edu/~dhowell/fundamentals8/DataFiles/Add.dat) are actual data on high school students. What is the 75th percentile for GPA in these data? (This is the point below which 75% of the observations are expected to fall.)
Assuming that the Behavior Problem scores discussed in this chapter come from a population with a mean of 50 and a standard deviation of 10, what would be a diagnostically meaningful cutoff if you wanted to identify those children who score in the highest 2% of the population? (Diagnostic cutoffs
On December 13, 2001, the Associated Press reported a story entitled “Study: American kids getting fatter at disturbing rate.” By 1998, nearly 22 percent of black children ages 4 to 12 were overweight, as were 22 percent of Hispanic youngsters and 12 percent of whites.. In 1986, the same survey
Using the distribution in Exercise 6.1, calculate z scores for X5 2.5, 6.2, and 9. Interpret these results.
Suppose that we are collecting a large data set on emotional reactivity in adults. Assume that for most adults emotional reactivity is normally distributed with a mean of 100 and a standard deviation of 10. But for people diagnosed with bipolar disorder, their scores are all over the place. Some
Use any Internet search engine to find a program that will generate normally distributed data and plot them.
Use the program you found in Exercise 6.23, or the programs available at www.danielsoper. com/statcalc3/ to verify a few of the entries in Table 6.1.
Most of you have had experience with exam scores that were rescaled so that the instructor could “grade on a curve.” Assume that a large Psychology 1 class has just taken an exam with 300 four-choice multiple-choice questions. (That’s the kind of Psychology 1 exam I took when I was but a lad.
Using the example from Exercise 6.3:(a) What two values of X (the count) would encompass the middle 50% of the results?(b) 75% of the counts would be less than ______.(c) 95% of the counts would be between _______ and _______.
Do you remember the earlier study by Katz et al. that had students answer SAT-type questions without first reading the passage? (If not, look at Exercises 3.1 and 4.1.) Suppose that we gave out the answer sheets for our Psychology 1 exam mentioned in Exercise 6.3 but forgot to hand out the
Students taking a multiple-choice exam rarely guess randomly. They usually can rule out some answers as preposterous and identify others as good candidates. Moreover, even students who have never taken Psychology 1 would probably know who Pavlov was, or what we mean by sibling rivalry. Suppose that
A set of reading scores for fourth-grade children has a mean of 25 and a standard deviation of 5. A set of scores for ninth-grade children has a mean of 30 and a standard deviation of 10. Assume that the distributions are normal. (a) Draw a rough sketch of these data, putting both groups in the
Under what conditions would the answers to (b) and (c) of Exercise 6.7 be equal?
Many diagnostic tests are indicative of problems only if a child scores in the upper 10 percent of those taking the test (at or above the 90th percentile). Many of these tests are scaled to produce T scores, with a mean of 50 and a standard deviation of 10. What would be the diagnostically
Give one example each of an analytic, a relative frequency, and a subjective view of probability.
I said that the probability of alcohol involvement, given an accident at night, was approximately .50, but I don’t know the probability of an accident, given that you had been drinking. How would you go about finding the answer to that question if you had sufficient resources?
In a study of the effectiveness of “please don’t litter” requests on supermarket fliers, Geller, Witmer, and Orebaugh (1976) found that the probability that a flier carrying a “do not litter” message would end up in the trash, if what people do with fliers is independent of the message
A graduate admissions committee has finally come to realize that it cannot make valid distinctions among the top applicants. This year the committee rated all 500 applicants and randomly chose 10 from those at or above the 80th percentile. (The 80th percentile is the point at or below which 80
With respect to Exercise 7.15, determine the conditional probability that the person will be admitted, given the following: a) That he or she has the highest rating b) That he or she has the lowest rating
In Appendix D (or the Add.dat data set on the website), what is the probability that a person drawn at random will have an ADDSC score greater than 50?
In Appendix D, what is the probability that a male will have an ADDSC score greater than 50?
In Appendix D, what is the probability that a person will drop out of school, given that he or she has an ADDSC score of at least 60?
Suppose that neighborhood soccer players are selling raffle tickets for $500 worth of groceries at a local store, and you bought a $1 ticket for yourself and one for your mother. The children eventually sold 1,000 tickets. a) What is the probability that you will win? b) What is the probability
Compare the conditional probability from Exercise 7.20 with the unconditional probability of dropping out of school.
People who sell cars are often accused of treating male and female customers differently. Make up a series of statements to illustrate simple, joint, and conditional probabilities with respect to such behavior. How might we begin to determine if those accusations are true?
Assume you are a member of a local human rights organization. How might you use what you know about probability to examine discrimination in housing?
Using the data from Exercise 7.25, compute the risk and odds ratios of punishment as a function of race.
Recently I had a call from a friend who is a lawyer in Vermont. He was representing an African- American client who was challenging the fairness of a jury selection. His concern was that African-Americans were not proportionately represented in the pool from which jurors are selected. In Vermont,
Now suppose that because of the high level of ticket sales, an additional $250 second prize will also be awarded. a) Given that you don’t win first prize, what is the probability that you will win second prize? (The first-prize ticket is not put back into the hopper before the second-prize ticket
Which parts of Exercise 7.3 dealt with joint probabilities? In Exercise 7.3 Now suppose that because of the high level of ticket sales, an additional $250 second prize will also be awarded. a) Given that you don’t win first prize, what is the probability that you will win second prize? (The
Which parts of Exercise 7.3 dealt with conditional probabilities? In Exercise 7.3 Now suppose that because of the high level of ticket sales, an additional $250 second prize will also be awarded. a) Given that you don’t win first prize, what is the probability that you will win second prize? (The
Make up a simple example of a situation in which you are interested in conditional probabilities. Frame the issue in terms of a research hypothesis.
In some homes a mother’s behavior seems to be independent of her baby’s and vice versa. If the mother looks at her child a total of 2 hours each day, and if the baby looks at the mother a total of 3 hours each day, and if they really do behave independently, what is the probability that they
In Exercise 7.8 assume that both mother and child sleep from 8:00 P.M. to 7:00 A.M. What would be the probability now?In Exercise 7.8In some homes a mother’s behavior seems to be independent of her baby’s and vice versa. If the mother looks at her child a total of 2 hours each day, and if the
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 I was discussing something other than a hockey score. In effect you have just tested and
Define “sampling error.”
What is the difference between a “distribution” and a “sampling distribution”?
Magen, 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
For the distribution in Figure 8.6, I said that the probability of a Type II error (b) is .64. Show how this probability was obtained.
Rerun the calculations in Exercise 8.14 for a 5 .01. In Exercise 8.14 For the distribution in Figure 8.6, I said that the probability of a Type II error (b) is .64. Show how this probability was obtained.
In the example in Section 8.10, what would we have done differently if we had chosen to run a two-tailed test?
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?
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.
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
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)
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
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?
Using the example in Exercise 8.2, describe what we mean by the rejection region and the critical value.
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?
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
In sub-Saharan Africa, more than half of mothers lose at least one child before the child€™s first birthday. Below are data on 36 countries in the region, giving country, infant mortality, per capita income (in U.S. dollars), percentage of births to mothers under 20, percentage of births
Down syndrome is another problem that psychologists deal with. It has been proposed that mothers who give birth at older ages are more likely to have a child with Down syndrome. Plot the data below relating age to incidence. The data were taken from Geyer (1991).Plot a scatter diagram for the
One way to get around the problem you see in Exercise 9.11 would be to convert the incidence of Down syndrome to ranked data. Replot the data using ranked incidence and calculate the correlation. Is this a Spearman’s correlation?
In the study by Katz et al., referred to previously, in which subjects answered questions about passages they had not read, the question arises as to whether there is a relationship between how the students performed on this test and how they had performed on the SAT-Verbal when they applied to

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