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essential statistics
Understanding Statistics In The Behavioral Sciences 10th Edition Robert R Pagano - Solutions
21. If two cards are randomly drawn from a deck of ordinary playing cards, one at a time, with replacement, what is the probability of obtaining at least one ace?other
20. A gumball dispenser has 38 orange gumballs, 30 purple ones, and 18 yellow ones. The dispenser operates such that one quarter delivers 1 gumball.a. Using three quarters, what is the probability of obtaining 3 gumballs in the order orange, purple, orange?b. Using one quarter, what is the
19. You are planning to win big at the race track. In a particular race, there are seven horses entered. If the horses are all equally matched, what is the probability of your correctly picking the winner and runner-up?other
18. You want to call a friend on the telephone. You remember the fi rst three digits of her phone number, but you have forgotten the last four digits. What is the probability that you will get the correct number merely by guessing once? other
17. You are playing the one-armed bandit (slot machine)described in Practice Problem 8.10, p. 212. There are three wheels, and on each wheel there is a picture of a lemon, a plum, an apple, an orange, a pear, cherries, and a banana (seven different pictures). You insert your silver dollar and pull
16. Answer the same questions as in Problem 15, except sampling is one at a time without replacement.other
15. If you are randomly sampling one at a time with replacement from a bag that contains eight blue marbles, seven red marbles, and fi ve green marbles, what is the probability of obtaininga. A blue marble in one draw from the bag?b. Three blue marbles in three draws from the bag?c. A red, a green,
14. If you roll two fair dice once, what is the probability that you will obtaina. A 2 on die 1 and a 5 on die 2?b. A 2 and a 5 without regard to which die has the 2 or 5?c. At least one 2 or one 5?d. A sum of 7? other
13. If you draw a single card once from a deck of ordinary playing cards, what is the probability that it will bea. The ace of diamonds?b. A 1 0?c. A queen or a heart?d. A 3 or a black card? other
12. At the beginning of the baseball season in a particular year, the odds that the New York Yankees will win the American League pennant are 3 to 2.a. What are the odds that the Yankees will lose the pennant?b. What is the probability that the Yankees will win the pennant? Express your answer as a
11. Which of the following are examples of exhaustive events?a. Flipping a coin and obtaining a head or a tail(edge not allowed)b. Rolling a die and obtaining a 2c. Taking an exam and either passing or failingd. Going out on a date and having a good time
10. Which of the following are examples of mutually exclusive events?a. Obtaining a 4 and a 7 in one draw from a deck of ordinary playing cardsb. Obtaining a 3 and a 4 in one roll of two fair dicec. Being male and becoming pregnantd. Obtaining a 1 and an even number in one roll of a fair diee.
9. Which of the following are examples of independent events?a. Obtaining a 3 and a 4 in one roll of two fair diceb. Obtaining an ace and a king in that order by drawing twice without replacement from a deck of cardsc. Obtaining an ace and a king in that order by drawing twice with replacement from
8. What is the defi nition of probability when the variable is continuous?
7. When solving problems involving the multiplication rule, is it useful to distinguish among three conditions?What are these conditions? Why is it useful to distinguish among them?
6. The addition rule gives the probability of occurrence of any one of several events, whereas the multiplication rule gives the probability of the joint or successive occurrence of several events. Is this statement correct? Explain, using examples to illustrate your explanation.
5. What is the difference between a priori and a posteriori probability?
4. A developmental psychologist is interested in assessing the “emotional intelligence” of college students.The experimental design calls for administering a questionnaire that measures emotional intelligence to a sample of 100 undergraduate student volunteers who are enrolled in an
3. Assume you want to form a random sample of 20 subjects from a population of 400 individuals. Sampling will be without replacement, and you plan to use Table J in Appendix D to accomplish the randomization. Explain how you would use the table to select the sample.
2. What two purposes does random sampling serve?
1. Defi ne or identify each term in the Important New Terms section.
2. A psychology professor is interested in the relationship between grade point average (GPA) in graduate school and Graduate Record Exam (GRE) scores. A random sample of 20 graduate students is used for the study. The GPA and GRE score for each student is shown in the table that follows.a. Use
1. For this example, let’s use the IQ and GPA (Grade Point Average) data shown in Table 7.2, p. 164, of the textbook. For your convenience the data is shown again here.a. Use SPSS to construct a scatter plot of the data. In so doing, name the two variables, IQ and GPA. Plot IQ on the X axis and
19. In Chapter 6, Problem 24 (p. 154), data were shown on the relationship between the work performance of 10 workers randomly chosen from the manufacturing section of a large corporation and two possible screening tests. The data are again shown below.In that problem you were asked to recommend
18. In Chapter 6, Problem 22 (p. 153), data were presented from a study conducted to determine the relationship between religious involvement and self-esteem. The data are again presented below.a. Assuming a linear relationship, derive the leastsquares regression line for predicting self-esteem
17. In Chapter 6, Problem 21 (p. 152), data were given on the relationship between the number of soft drinks consumed in a week by eight 12-year-olds and their body mass index (BMI). The 12-year-olds were randomly selected from a junior high school in a large northwestern city. The data are again
16. In Chapter 6, Problem 16 (p. 151), data were presented on the relationship between birth weight and the subsequent IQ of seven randomly selected psychology majors from a particular university. The data are again presented below.Student Birth Weight (lbs) IQ 1 5.8 122 2 6.5 120 3 8.0 129 4 5.9
15. During infl ationary times, Mr. Chevez has become budget conscious. Since his house is heated electrically, he has kept a record for the past year of his monthly electric bills and of the average monthly outdoor temperature. The data are shown in the following table. Temperature is in degrees
14. A newspaper article reported that “there is a strong correlation between continuity and success when it comes to NBA coaches.” The article was based on the following data:a. Is the article correct in claiming that there is a strong correlation between continuity and success when it comes to
13. The sales manager of a large sporting goods store has recently started a national advertising campaign. He has kept a record of the monthly costs of the advertising and the monthly profi ts. These are shown here.The entries are in thousands of dollars.Month Jan. Feb. Mar. Apr. May Jun.
12. A statistics professor conducts a study to investigate the relationship between the performance of his students on exams and their anxiety. Ten students from his class are selected for the experiment. Just before taking the fi nal exam, the 10 students are given an anxiety questionnaire. Here
11. A popular attraction at a carnival recently arrived in town is the booth where Mr. Clairvoyant (a bright statistics student of somewhat questionable moral character) claims that he can guess the weight of females to within 1 kilogram by merely studying the lines in their hands and fi ngers. He
10. A clinical psychologist is interested in the relationship between testosterone level in married males and the quality of their marital relationship. A study is conducted in which the testosterone levels of eight married men are measured. The eight men also fi ll out a standardized questionnaire
9. Given the set of paired X and Y scores,a. Construct a scatter plot of the paired scores. Does the relationship appear linear?b. Determine the least-squares regression line for predicting Y given X.c. Draw the regression line on the scatter plot.d. Using the relationship between X and Y, what
8. What is R2 called? Is it true that conceptually R2 is analogous to r2, except that R2 applies to situations in which there are two or more predictor variables? Explain.Will using a second predictor variable always increase the precision of prediction? Explain.
7. Of what value is it to know the standard error of estimate for a set of paired X and Y scores?
6. How are r and bY related? Explain.
5. State the convention that is used to assign X and Y to the predicted to and predicted from variables.
4. The least-squares regression line is the prediction line that results in the most direct “hits.” Is this statement correct? Explain.
3. The least-squares regression line minimizes (Y Y')2 rather than (Y Y'). Is this statement correct?Explain.
2. List some situations in which it would be useful to have accurate prediction.
1. Defi ne or identify each of the terms in the Important New Terms section.
2. A psychology professor is interested in whether there is a relationship between reaction time and age. The following data are collected on thirty individuals randomly sampled from the city in which the professor works. Random sampling is conducted in a manner to ensure that a wide age range is
1. For this problem, we will use the data given in Chapter 6, Problem 19, p. 152.a. Use SPSS to construct a scatter plot of the data.Name the variables American and Italian. Use American as the X axis variable and Italian as the Y axis variable.b. Describe the relationship.c. Use SPSS to calculate
24. For this problem, let’s suppose that you are a psychologist employed in the human resources department of a large corporation. The corporation president has just fi nished talking with you about the importance of hiring productive personnel in the manufacturing section of the corporation and
23. A psychologist has constructed a paper & pencil test purported to measure depression. To see how the test compares with the ratings of experts, 12 “emotionally disturbed” individuals are given the paper &pencil test. The individuals are also independently rank-ordered by two
22. A social psychologist conducts a study to determine the relationship between religion and selfesteem.Ten eighth graders are randomly selected for the study. Each individual undergoes two tests, one measuring self-esteem and the other religious involvement. For the self-esteem test, the lower
21. The director of an obesity clinic in a large northwestern city believes that drinking soft drinks contributes to obesity in children. To determine whether a relationship exists between these two variables, she conducts the following pilot study.Eight 12-year-old volunteers are randomly selected
20. Given the following set of paired scores from fi ve subjects,a. Construct a scatter plot of the data.b. Compute the value of Pearson r.c. Add the following paired scores from a sixth subject to the data: Y 26, X 25.d. Construct another scatter plot, this time for the six paired scores.e.
19. A group of researchers has devised a stress questionnaire consisting of 15 life events. They are interested in determining whether there is crosscultural agreement on the relative amount of adjustment each event entails. The questionnaire is given to 300 Americans and 300 Italians. Each
18. An educator has constructed a test for mechanical aptitude. He wants to determine how reliable the test is over two administrations spaced by 1 month.A study is conducted in which 10 students are given two administrations of the test, with the second administration being 1 month after the fi
17. A researcher conducts a study to investigate the relationship between cigarette smoking and illness. The number of cigarettes smoked daily and the number of days absent from work in the last year due to illness is determined for 12 individuals employed at the company where the researcher works.
16. A graduate student in developmental psychology believes there may be a relationship between birth weight and subsequent IQ. She randomly samples seven psychology majors at her university and gives them an IQ test. Next she obtains the weight at birth of the seven majors from the appropriate
15. In a large introductory sociology course, a professor gives two exams. The professor wants to determine whether the scores students receive on the second exam are correlated with their scores on the fi rst exam. To make the calculations easier, a sample of eight students is selected. Their
14. Given the following sets of paired sample scoresa. Use the equation r © zXzY1N 12 to compute the value of Pearson r for each set. Note that in set B, where the correlation is lowest, some of the zXzY values are positive and some are negative.These tend to cancel each other, causing r to
13. What effect does decreasing the range of the paired scores have on the correlation coeffi cient?
12. What effect might an extreme score have on the magnitude of relationship between two variables?Discuss.
11. When two variables are correlated, there are four possible explanations of the correlation. What are they?
10. The Pearson r and Spearman rho correlation coeffi -cients are related. Is this statement correct? Explain.
9. What factors infl uence the choice of whether to use a particular correlation coeffi cient? Give some examples.
8. A study has shown that the correlation between fatigue and irritability is 0.53. On the basis of this correlation, the author concludes that fatigue is an important factor in producing irritability. Is this conclusion justifi ed?Explain.
7. What is the range of values that a correlation coeffi cient may take?
6. Why are z scores used as the basis for determining Pearson r?
5. Give two meanings of Pearson r.
4. Professor Taylor does an experiment and establishes that a correlation exists between variables A and B. On the basis of this correlation, she asserts that A is the cause of B. Is this assertion correct? Explain.
3. For each scatter plot in the accompanying fi gure(parts a–f, on p. 150), determine whether the relationship isa. Linear or curvilinear. If linear, further determine whether it is positive or negative.b. Perfect or imperfect
2. Discuss the different kinds of relationships that are possible between two variables.
1. Defi ne or identify each of the terms in the Important New Terms section.
3. When fi nished, click “Grade It Now” to see which areas you have mastered and which need more work, and for detailed explanations of every answer.
2. Complete the corresponding homework exercises as required by your professor
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3. Use SPSS to demonstrate that the mean of a z distribution of scores equals 0 and the standard deviation equals 1.
2. Use SPSS to compute z scores for the distance scores given in Chapter 5, Problem 20, p. 118 in the textbook.Compare your answer with that given in Appendix C for this problem. Name the scores Distance.
1. Use SPSS to compute z scores for the following data set. In solving the problem, name the scores Y.10, 13, 15, 16, 18, 20, 21, 24
24. A psychologist interested in the intelligence of children develops a standardized test for selecting “gifted”children. The test scores are normally distributed, with 75 and 8. Assume a gifted child is defi ned as one who scores in the upper 1% of the distribution.What is the minimum
23. On which of her two exams did Rebecca do better?How about Maurice? Assume the scores on each exam are normally distributed. Rebecca’s Scores Maurice’s Scores Exam 1 120 6.8 130 132 Exam 2 50 2.4 56 55 education
22. Anthony is deciding whether to go to graduate school in business or law. He has taken nationally administered aptitude tests for both fi elds. Anthony’s scores along with the national norms are shown here. Based solely on Anthony’s relative standing on these tests, which fi eld should he
21. A stock market analyst has kept records for the past several years of the daily selling price of a particular blue-chip stock. The resulting distribution of scores is normally shaped with a mean μ $84.10 and a standard deviation $7.62.a. Determine the percentage of selling prices that
20. A jogging enthusiast keeps track of how many miles he jogs each week. The following scores are sampled from his year 2007 records:Week Distance* Week Distance 5 32 30 36 8 35 32 38 10 30 38 35 14 38 43 31 15 37 48 33 19 36 49 34 24 38 52 37*Scores are miles run.a. Determine the z scores for the
19. Using the same population parameters as in Problem 17, fi nd what percentage of scores are between the following scores:a. 6.8 and 10.2b. 5.4 and 8.0c. 8.8 and 10.5 I/O, other
18. Using the same population parameters as in Problem 17, fi nd what percentage of scores are above the following scores:a. 10.5b. 13.8c. 7.6d. 3.5e. 8.2 I/O, other
17. A statistician studied the records of monthly rainfall for a particular geographic locale. She found that the average monthly rainfall was normally distributed with a mean μ 8.2 centimeters and a standard deviation 2.4. What is the percentile rank of the following scores?a. 12.4b. 14.3c.
16. A hospital in a large city records the weight of every infant born at the hospital. The distribution of weights is normally shaped, with a mean μ 2.9 kilograms and a standard deviation 0.45. Determine the following:a. The percentage of infants who weighed less than 2.1 kilogramsb. The
15. At the end of a particular quarter, Carol took four fi nal exams. The mean and standard deviation for each exam along with Carol’s grade on each exam are listed here. Assume that the grades on each exam are normally distributed.Exam Mean Standard Deviation Carol’s Grade French 75.4 6.3 78.2
14. Given that a population of scores is normally distributed with μ 110 and 8, determine the following:a. The percentile rank of a score of 120b. The percentage of scores that are below a score of 99d. 4.1e. 8.2 I/O, other
13. For each of the following, determine the z score that divides the distribution such that the given percentage of scores lies above the z score (round to two decimal places):a. 50%b. 2.50%c. 5%d. 30%e. 80%f. 90%
12. For the following z scores, determine the percentage of scores that lie between the mean and the z score:a. 1b. –1c. 2.34d. –3.01e. 0f. 0.68 g. –0.73
11. For the following z scores, determine the percentage of scores that lie beyond z:a. 0b. 1c. 1.54d. –2.05e. 3.21f. –0.45
10. A population of raw scores is normally distributed with μ 60 and 14. Determine the z scores for the following raw scores taken from that population:a. 76b. 48c. 86d. 60e. 74f. 46
9. Assume the raw scores in Problem 8 are population scores and perform the calculations called for in parts a and b.
8. Given the set of sample raw scores 10, 12, 16, 18, 19, 21,a. Convert each raw score to its z-transformed value.b. Compute the mean and standard deviation of the z scores.
7. What proportion of scores in a normal distribution will have values lower than z 0? What proportion will have values greater than z 0?
6. If a set of scores is normally distributed, what information does the area under the curve give us?
5. Are all bell-shaped distributions normal distributions?Explain.
4. Must the shape of a z distribution be normal? Explain.
3. What are the values of the mean and standard deviation of the z distribution?
2. What is a score transformation? Provide an example.
1. Defi nea. Asymptoticb. The normal curvec. z scoresd. Standard scores
3. Use SPSS to demonstrate that the standard deviation of a set of scores can vary without changing the mean.
2. Use SPSS to demonstrate that the mean of a set of scores can vary without changing the standard deviation.
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