Basic Statistics For The Behavioral Sciences 5th Edition Gary Heiman - Solutions

4. What is the general form of the linear regression equation? Identify its component symbols.
3. What is Y' and how do you obtain it?
2. What is the linear regression procedure used for?
1. What is the linear regression line?
23. A researcher observes the behavior of a group of monkeys in the jungle. He determines each monkey’s relative position in the dominance hierarchy of the group (1 being most dominant) and also notes each monkey’s relative weight (1 being the lightest). What is the relationship between
22. In the following data, the X scores reflect participants’ rankings in a freshman class, and the Y scores reflect their rankings in a sophomore class. To what extent do these data form a linear relationship? {Caution: Think before you calculate.)Participant Fresh.X Soph.Y 12 32 97 31 24 57
21. You want to know if a nurse’s absences from work in one month (Y) can be pre¬ dicted by knowing her score on a test of psychological “burnout” (Y). What do you conclude from the following ratio data?Participant Burnout XAbsences Y1 24 21 13 26 43 95 46 64 87 77 87 10 98 11
20. A researcher measures the following scores for a group of people. The X variable is the number of errors on a math test, and the Y variable is the person’s level of satisfaction with his/her performance, (a) With such ratio scores, what should the researcher conclude about this relationship?
19. A researcher has just completed a correlational study, measuring participants’ general level of aggression and the number of times their driving showed “road rage” today, (a) Which is the independent and the dependent variable? (b) Which variable is X? Which is Y?
18. We obtain a correlation of +.20 after measuring a sample of creativity test scores and intelligence test scores, (a) Can we conclude that this is similar to the rela¬ tionship we’d find between all similar participants found in nature? (b) Once we have performed the necessary procedures,
17. Foofy and Poindexter study the relationship between IQ score and high school grade average, measuring a large sample of students from PEST (the Program for Exceptionally Smart Teenagers), and compute r = +.03. They conclude that there is virtually no relationship between IQ and grade average.
16. In the correlation between orange juice consumed and number of doctor visits discussed in this chapter, does drinking more orange juice cause people to be more healthy so that they don’t have to go to the doctor?
15. Poindexter finds that r = —.40 between the variables of number of hours studied and number of errors on a statistics test. He also finds that r = + .36 between the variables of time spent taking the statistics test and the number of errors on the test. He concludes that the time spent taking
14. For each of the following, give the symbol for the correlation coefficient you should compute. You measure (a) SAT scores and IQ scores; (b) taste rankings of tea by experts and those by novices; (c) finishing position in a race and amount of liquid consumed during the race.
13. Poindexter sees the data in question 12d and concludes, “We should stop people from moving into bear country so that we can preserve our bear population.” What is the problem with Poindexter’s conclusion?
12. For each of the following, indicate whether it is a positive linear, negative linear, or nonlinear relationship: (a) Quality of performance (7) increases with increased arousal (X) up to an optimal level; then quality of performance decreases with increased arousal, (b) Overweight people (X)
11. (a) What does p stand for? (b) How is the value of p determined? (c) What does p tell you?
10. (a) What is the restriction of range problem? (b) What produces a restricted range? (c) How is it avoided?
9. What does a correlation coefficient equal to 0 indicate about the four characteris¬ tics in question 8?
8. As the value of r approaches ±1, what does it indicate about the following?(a) The consistency in the X-Y pairs; (b) the variability of the Y scores at each X; (c) the closeness of Y scores to the regression line; (d) the accuracy with which we can predict 7 if X is known.
7. (a) Define a positive linear relationship, (b) Define a negative linear relationship, (c) Define a curvilinear relationship.
6. Why can’t you obtain a correlation coefficient greater than ±1?
5. (a) What is a scatterplot? (b) What is a regression line?
4. (a) When do you compute a Pearson correlation coefficient? (b) When do you compute a Spearman coefficient?
3. What are the two reasons why you can’t conclude you have demonstrated a causal relationship based on correlational research?
2. (a) You have collected data that you think show a relationship. What do you do next? (b) What is the advantage of computing a correlation coefficient? (c) What two characteristics of a linear relationship are described by a correlation coefficient?
1. What is the difference between an experiment and a correlational study in terms of how the researcher (a) Collects the data? (b) Examines the relationship?
25. In a study, you first collect these raw scores:86 85 73 71 67 88 57 57 45 60(a) You are about to test 200 more people. How many do you expect will score below 65? (b) How many do you expect to score above 70? (c) After collecting these additional scores, you find your expectations in parts (a)
24. Using the test in question 2% you measure 64 children, obtaining a A of 57.28. Slug says that because this X is so close to the p, of 56, this sample could hardly be considered gifted, (a) Perform the appropriate statistical procedure to deter¬ mine whether he is correct, (b) In what
23. A researcher develops a test for selecting intellectually gifted children, with a p, of 56 and a of 8. (a) What percentage of children are expected to score below 60? (b) What percentage of scores will be above 54? (c) A gifted child is defined as being in the top 20%. What is the minimum test
22. Suppose you own shares of a company’s stock, the price of which has risen so that, over the past ten trading days, its mean selling price is $14.89. Over the years, the mean price of the stock has been $10.43 (ct^ = $5.60). You wonder if the mean selling price over the next ten days can be
21. A recent graduate has two job offers and must decide which to accept. The job in city A pays $27,000. The average cost of living there is $50,000, with a standard deviation of $15,000. The job in city B pays $12,000. The average cost of living there is $14,000, with a standard deviation of
20. For an IQ test, we know the population p. = 100 and the = 16. We are inter¬ ested in creating the sampling distribution when N = 64. (a) What does that sam¬ pling distribution of means show? (b) What is the shape of the distribution of IQ means and the mean of the distribution? (c) Calculate
19. Poindexter may be classified as having a math dysfunction—and not have to take statistics—if he scores below the 25th percentile on a diagnostic test. The p, of the test is 75 (a^ = 10). Approximately what raw score is the cutoff score for him to avoid taking statistics?
18. For a distribution in which X = 100, 5;^^ = 16, and N = 500, answer the fol¬ lowing: (a) What is the relative frequency of scores between 76 and the mean?(b) How many participants are expected to score between 76 and the mean?(c) What is the percentile of someone scoring 76? (d) How many
17. In a normal distribution, what proportion of all scores would fall into each of the following areas? (a) Between the mean and z = +1.89; (b) below z = —2.30;(c) between z = -1.25 and z = +2.75; (d) above z = +1.96 and below -1.96.
16. For each pair in question 15, which z-score has the higher frequency?
15. Which z-score in each of the following pairs corresponds to the lower raw score?(a) z = +1.0 or z = +2.3; (b) z = -2.8 or z = -1.7; (c) z = -.70 or z = +.20; (d) z = 0.0 or z = —2.0.
14. For the data in question 13, find the raw scores that correspond to the following: (a)z = +1.22; (b) z = -0.48.
13. For the data, 9 5 10 7 9 10 11 8 12 7 6 9(a)Compute the z-score for the raw score of 10. (b) Compute the z-score for the raw score of 6.
12. Foofy computes z-scores for a set of normally distributed exam scores. She obtains a z-score of —3.96 for 8 out of 20 of the students. What does this mean?
11. I^indexter received a 55 on a biology test (X = 50) and a 45 on a philosophy test (X = 50). He is considering whether to ask his two professors to curve the grades using z-scores. (a) What other information should he consider before making his request? (b) Does he want the to be large or small
10. In an English class last semester, Foofy earned a 76 (X = 85, = 10). Her friend. Bubbles, in a different class, earned a 60 (X = 50, = 4). Should Foofy be bragging about how much better she did?_Why?
9. (a) What are the steps for using the standard normal curve to find a raw score’s relative frequency or percentile? (b) What are the steps for finding the raw score that cuts off a specified relative frequency or percentile? (c) What are the steps for finding a sample mean’s relative
8. What does the standard error of the mean indicate?
7. What three things does the central limit theorem tell us about the sampling distri¬ bution of means? (b) Why is this so useful?
6. (a) What is a sampling distribution of means? (b) When is it used? (c) Why is it useful?
5. (a) What is the standard normal curve? (b) How is it applied to a set of data?(c) What three criteria should be met for it to give an accurate description of a sample?
4. What are the three general uses of z-scores with individual raw scores?
3. What is a z-distribution?
2. On what two factors does the size of a z-score depend?
1. (a) What does a z-score indicate? (b) Why are z-scores important?
26. Comparing the results in questions 21 and 24, which experiment produced the stronger relationship? How do you know?
25. Say that you conducted the experiment in question 24 on the entire population, (a) Summarize the relationship that you’d expect to observe, (b) How consis¬ tently do you expect participants to behave in each condition?
24.Consider these ratio scores from an experiment:Condition 1 Condition 2 Condition 3 18 83 13 11 99 65(a) What should you do to summarize the experiment? (b) Summarize the relationship in the sample data, (c) How consistent were participants in each condition?
23. In two studies, the mean is 40; in Study A, = 5, and in Study B, = 10.(a) What is the difference in the appearance of the distributions from these studies? (b) Where do you expect the majority of scores to fall in each Study?
22. Say that you conducted the experiment in question 21 on the entire population, (a) Summarize the relationship that you’d expect to observe, (b) How consis¬ tently do you expect participants to behave in each condition?
21. Consider the results of this experiment:Condition A Condition B Condition C 12 33 47 11 33 48 11 34 49 10 31 48(a) What “measures” should you compute to summarize the experiment?(b) These are ratio scores. Compute the appropriate descriptive statistics and summarize the relationship in the
20. Say that the teacher in question 19 finds that the relationship between study times and exam scores accounts for .40 of the variance in exam scores. What does this mean?
19. If the teacher in question 18 compares the error when using study times to predict exam scores to the error when using the overall mean exam score to predict exam scores, what statistical information is she computing?
18. The teacher who gave the test in question 17 found a relationship between students’ scores and the amount they studied. If she uses her knowledge of each student’s study time to predict the corresponding exam grade, what will happen to her average error relative to the error described in
17. On a final exam the X = 65 and = 6. What score would you predict for each student, and if you’re wrong, what do you expect will be the average error in your prediction?
16. I correctly compute the variance of a distribution to be = 0. What should you conclude about this distribution?
15. From his statistics grades, Guchi has a X of 60 and = 20. Pluto has a X of 60 and = 5. (a) Who is the more inconsistent student, and why? (b) Who is more accurately described as a 60 student, and why? (c) For which student can you more accurately predict the next test score, and why? (d) Who is
14.Foofy has a normal distribution of scores ranging from 2 to 9. (a) She computed the variance to be —.06. What should you conclude from this answer, and why? (b) She recomputes the standard deviation to be 18. What should you conclude, and why? (c) She recomputes the variance to be 1.36. What
13. If you could test the population in question 12, what would you expect each of the following to be? (a) The shape of the distribution; (b) the typical, most com¬ mon rate; (c) the variance; (d) the standard deviation; (e) the two scores between which about 68% of all heart rates fall.
12. As part of studying the relationship between mental and physical health, you obtain the following heart rates:73 72 67 74 78 84 79 71 76 76 79 81 75 80 78 76 78 In terms of differences in heart rates, interpret these data using the following:(a) the range, (b) the variance, and (c) the standard
11. Say the sample in question 9 had an N of 1000. About how many people would you expect to score below 1.59? Why?
10. If you could test the entire population in question 9, what would you expect each of the following to be? (a) The typical, most common creativity score; (b) the variance; (c) the standard deviation; (d) the two scores between which about 68% of all creativity scores occur in this situation.
9. In a condition of an experiment, a researcher obtains the following creativity scores:3210748664 In terms of creativity, interpret the variability of these data using the following: (a) the range, (b) the variance, and (c) the standard deviation.
8. In an experiment, how does the size of in each condition suggest the strength of the relationship?
7. Why are your estimates of the population variance and standard deviation always larger than the corresponding values that describe a sample from that population?
6. (a) What do 5^, 5^, and cr^ have in common in terms of what they communicate? (b) How do they differ in terms of their use?
5. (a) What is the mathematical definition of the variance? (b) Mathematically, how is a sample’s variance related to its standard deviation and vice versa?
4. (a) What do both the variance and the standard deviation tell you about a distri¬ bution? (b) Which measure will you usually want to compute? Why?
3. (a) What is the range? (b) Why is it not the most accurate measure of variability? (c) When is it used as the sole measure of variability?
2. What do measures of variability communicate about (a) the size of differences between the scores in a distribution and (b) how consistently the participants behaved?
1. (a) In any research, what three characteristics of a distribution must the researcher describe? (b) Why is describing the variability important?
26. Assume that the data in question 25 reflect a highly skewed interval variable.(a) Compute the summaries of these scores, (b) What conclusion would you draw from the sample data? (c) What conclusion would you draw about the popula¬ tions produced by this experiment?
25. You conduct a study to determine the impact that varying the amount of noise in an office has on worker productivity. You obtain the following productivity scores.Condition 1: Low Noise Condition 2: Medium Noise Condition 3: Loud Noise 15 13 12 19 11 913 14 713 10 8(a) Assuming that
24. You hear that a line graph of data from the Grumpy Emotionality Test slants downward as a function of increases in the amount of sunlight present on the Application Questions 87 day participants were tested, (a) What does this tell you about the mean scores for the conditions? (b) What does
23. For each of the experiments listed below, determine (1) which variable should be plotted on the Y axis and which on the X axis, (2) whether the researcher should use a line graph or a bar graph to present the data, and (3) how she should summarize scores on the dependent variable: (a) a study
22. (a) In question 21, give a title to the graph, using “as a function of.’’ (b) If you participated in the study in question 21 and had been deprived of 5 hours of sleep, how many errors do you think you would make? (c) If we tested all people in the world after 5 hours of sleep
21. For the following experimental results, interpret specifically the relationship between the independent and dependent variables:
20. What is p, and how do we usually determine its value?
19. Foofy says a deviation of +5 is always better than a deviation of —5. Why is she correct or incorrect?
18. In a normal distribution of scores, five participants obtained the following deviation scores: +1, —2, +5, and —10. (a) Which score reflects the highest raw score?(b) Which score reflects the lowest raw score? (c) Rank-order the deviation scores in terms of their frequency, starting with
17. On a normal distribution of scores, four participants obtained the following deviation scores: —5, 0, +3, and +1. (a) Which person obtained the lowest raw score? How do you know? (b) Which person’s raw score had the lowest frequency? How do you know? (c) Which person’s raw score had the
16. You misplaced two of the scores in a sample, but you have the data indicated below. What should you guess the missing scores to be? Why?100 120 130 140 no 140 150 130 120 130
15. A researcher collected the following sets of data. For each, indicate the measure of central tendency she should compute: (a) the following IQ scores: 60, 72, 63, 83, 68, 74, 90, 86, 74, and 80; (b) the following error scores: 10, 15, 18, 15, 14, 13, 42, 15, 12, 14, and 42; (c) the following
14. (a) In question 13, what is your best estimate of the median (without computing it)? (b) Explain why you think your answer is correct, (c) Calculate the approximate median using the method described in this chapter.
13. For the following data, compute (a) the mean and (b) the mode.55 57 59 58 60 57 56 58 61 58 59
12. (a) When graphing an experiment, which variable is on the X axis and which is on y? (b) When are bar graphs or line graphs appropriate?
11. (a) What is the symbol for a score’s deviation from the mean? (b) What is the symbol for the sum of the deviations? (c) What does it mean to say “the sum of the deviations around the mean equals zero”?
10. Why do we use the mean of a sample to predict any score that might be found in that sample?
9. What two pieces of information about the location of a score does a deviation score convey?
8. Which measure of central tendency is used most often in behavioral research? Why?
7. Why is it inappropriate to use the mean with a skewed distribution?
6. Why is it best to use the mean with a normal distribution?
5. What is the mean, and with what type of data is it most appropriate?

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Basic Statistics For The Behavioral Sciences 5th Edition Gary Heiman - Solutions

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