Exam Review Fall 2013

7/26/2019 Exam Review Fall 2013

1/12

PSYC204

INTRODUCTION TO PSYCHOLOGICAL STATISTICS

EXTRA PRACTICE REVIEW PROBLEMS

1. In a political survey of 500 people, a researcher obtained the geographic locations andopinions shown. What is the probability of being from NB or voting YES or both?

VOTE

LOCATION YES NO

NB 160 40BC 40 160NS 25 75

2. School A has mean grade of 80 on an entrance exam with s = 5. School B has a meangrade of 70 with s = 10. The scores in each school are normally distributed. Whatpercentage of students in school B do better than the average student in school A?

3. Fingerprints vary on many dimensions, including the number of ridges. The distributionfor number of ridges is normal with a mean of 165 and standard deviation of 10.Approximately what proportion of the population would be expected to have a ridge countgreater than 191?

4. An experimenter finds that a sample of 100 workers have a mean income of $30,000 with astandard deviation of 4,000. He is 68% sure that the mean income of the population isbetween:

5. It is known from experience that 20% of all people who get a certain mail-order cataloguewill order something. If 4 people get the catalogue, find the probability that 2 will ordersomething.

6.For X1= 1 Y1 = 4 ( !X

2)+( !Y)2=

X2 = 2 Y2 = -2


2/12

7. The probability is .70 that a rare tropical disease will be treated correctly. If it is treatedcorrectly, the probability is .90 that the patient will be cured. If it is not treated correctly,the probability is only .40 that the patient will be cured. What is the probability that apatient having this disease will be cured?

8. Five students write an exam. Four of them report their deviation scores to be 1, 3, -1 and 5.The fifth wont talk about the exam. Without knowing the mean, can you calculate the

fifth deviation score and the variance of the raw (not deviation) scores? If so, perform thecalculation. If not, use the formula for variance to explain.

9. You are registered for a course where studying has no effect on grades, which are assignedcompletely at random. If the probability of studying is .1 and the probability of passingwith at least a B is .6, whats the probability that you study or pass with at least a B?

10. An instrument measures anxiety in students on a scale of -50 to +50. This class has a meanof 8 and a standard deviation of 2. Your deviation score is 5. During summer for reasonsthat are inexplicable, the scores of everyone in class were multiplied by -3. What would be

the new class mean and variance? What would be your new deviation score? What wouldbe your old and new standard scores?

11. Calculate the mean and variance for X, where X is number of weekend study hours.

12. A deck consists of ten cards numbered 1 through 10. In a game, you pull one card at atime, replacing the card after each draw. You win if the third 4 appears on the fifth draw.That is, you must get two 4s in the first four draws and then get another 4. Whats theprobability of winning?

13. A regression line predicting exam grade from the time it takes to write the exam has anequation Y = 1 X + 5. What, if anything, do you know about the correlation betweenexam grade and writing time? What do you not know?

For the same problem, if you are given s2y= 3, and s2y.x= 1, does this improve your ability

to calculate r? Show the calculation or explain.

14. During four consecutive years of operation, a companys gross income from sales was 1, 2,2 and 3 million dollars. For those four years, the correlation between sales income andnumber of years in operation is:

X f

9 11 106 8 103 5 20


3/12

15. A statistician who was about to buy a dog conducted a study on the relationship between

the size of dogs measured in pounds and scores on a canine halitosis scale where highscores indicate bad breath. Ten neighborhood dogs were included in the survey and thedata are tabled below:a) Calculate the correlation between size and halitosis.b) Calculate the regression equation to predict halitosis from size. Table dependent andindependent variables, estimates and residuals.

c) Calculate the standard error of estimation. How much of the variability in halitosis canbe accounted for by the size of the dog.d) The statistician decided to purchase a dog with an expected adult weight of 80 lbs.Estimate the halitosis score for this dog and discuss the limitations of this estimate.

Size Halitosis

5 4015 6530 8520 3040 100

35 6045 7030 4540 8510 10

16. The following probability table is from the Digest of Educational Statistics

STATUS

Engineer ScientistBachelors .343 .289 .632

HIGHEST Masters .098 .146 .244DEGREE Doctorate .017 .091 .108

Other .013 .003 .016

.471 .529

What is the probability that a person chosen at random from this group:

a) has a doctorate?b) is a scientist and has a doctorate?c) is an engineer or has a doctorate?d) has (only) a bachelors given that the person is a scientist?


4/12

17. The Nielsen Report shows the mean weekly TV viewing time for children of ages 2 - 5years as being 27 hours. Assume this viewing time is normally distributed with a standarddeviation of 6 hours. Then

a) 95% of such children watch between ______ and ______ hours of TV per week.b) ______% of such children watch less then 30 hours of TV per week.

18. In the following table are annual starting salaries of 8 randomly selected accountinggraduates and 10 graduates in liberal arts. Data are given in thousands of dollars roundedto the nearest hundred.

Accounting Liberal Arts

24.9 20.4 23.3 20.9 20.0 16.8 21.3 20.6 21.0

23.4 25.3 26.8 22.6 18.7 23.8 18.3 17.7 18.0

a) Determine whether the data provide evidence of a difference between accountinggraduates and liberal arts graduates on annual starting salaries.

b) Perform a test of homogeneity of variance. Write a short summary of the study statingthe purpose, variables, used, test statistics and conclusions.

19. A golf magazine conducted a study to compare the driving distances for two brands of golfballs. Ten professional golfers drove one ball of each brand and recorded their distances inyards. Is there evidence of a difference?

Pr

o

Brand A Brand B

1 283 287

2 268 2723 287 3054 249 2405 290 2936 297 2827 257 2578 235 2419 316 32410 317 310


5/12

20. A statistical process control expert wants to know whether the diameters of bolts producedby a machine are normally distributed. He takes a random sample of 265 bolts and findsthat the mean is 10.00 mm and s = .10 mm. The frequency distribution is as follows:

Diameter Observed frequency

under 9.8 89.8 under 9.9 42

9.9 under 10.0 11210 under 10.1 97

10.1 under 10.2 3

10.2 and over 3

Can the expert conclude that the bolts are not normally distributed?

21. A professor wants to compare the effectiveness of two texts in teaching statistics. Thechoice of text left to the students. The information below represents the student faculty

(Arts or Science), text (Old or New) and final grade for a sample of 20 students.

Faculty Text Grade Faculty Text Grade

A O 75 A O 65

A O 71 S O 82

S O 65 A O 76

A O 71 S O 88

S O 69 A O 67

A N 68 A N 67

S N 29 A n 65A N 66 S N 62

A N 35 A N 24

A N 61 S N 60

Was the choice of text related to the students faculty?Did the students differ in final grades according to faculty ?Did the students differ in final grades according to which text they used?Write a short paragraph summarizing your findings.


6/12

22. A survey was sent to the TAs in a Psychology Department asking how much time they spenton TA activities in an average week. The responses were as follows, rounded to the nearesthour (some TAs do not teach):

6 hrs. 13 hrs. 2 hrs. 14 hrs. 7 hrs.12 hrs. 14 hrs. 4 hrs. 6 hrs.. 2 hrs.13 hrs. 12 hrs. 13 hrs. 16 hrs. 1 hr.

a) Calculate the mean, median and mode of this ungrouped data.b) Calculate the range, mean deviation and standard deviation of the ungrouped data.c) Calculate the deviation score and the standard score for a student who spends 10 hourson TA activities.d) The Department assumes that TAs spend no more than 10 hours per week on TAactivities. Test the hypothesis and make a brief report.

23. In a recent evaluation of an advanced statistics text, students were asked to rate the text on a

scale of 1 (poor) to 10 (excellent). Scales such as this are often treated as interval data. Thedistribution of scores is tabled below:

Rating f

9 - 10 427 - 8 315 6 163 4 71 2 4

a) From the grouped data, calculate the mean, median, variance and standard deviation.

b) What is the rating for a student whose standard score is about -2.5?c) If we changed the rating scale so that it went from 0 - 9 instead of 1 - 10, that is wesubtracted 1 from each rating, how would this change the values for the statistics in (a)? Ifwe changed the rating scale by multiplying each rating by two, how would this change thevalues for the statistics in (a)?


7/12

24. One of my students made the claim that a course can be good even when the instructor is

not. I think that the two are related to some extent. Here is a set of data on class averagesfrom a course evaluation, based on a 0 - 100 scale.

Rate course (low=poor) Rate instructor (low=poor)

82 8266 76

64 6870 9080 4854 7892 7878 7074 8080 72

a) Calculate the correlation (coefficient) for this set of data and test its significance.Comment on what this reveals about the relationship between course and instructor ratings.

25. Prepare a frequency distribution with a class interval of 5. Show also the cumulativefrequency distribution and cumulative percentage frequencies. The following arehypothetical scores made by students on a multiple choice examination:

87 76 73 70 67 66 64 63 61 60

85 75 72 69 67 65 64 62 61 60

82 74 71 69 67 65 63 62 61 60

78 74 71 68 66 65 63 62 61 60

77 74 70 68 66 64 63 62 61 60

60 59 58 57 56 54 52 50 46 4360 59 58 57 55 54 52 49 46 42

60 59 58 57 55 53 51 49 46 38

60 59 58 56 55 53 51 48 45 35

60 59 57 56 54 53 50 37 44 33


8/12

26. The following is a frequency distribution of reaction time measurements:

Class Interval f

70-79 2

60-69 2

50-59 4

40-49 6

30-39 2

20-29 3

10-19 1

20

Obtain (a) the exact limits of the class intervals

(b) the midpoints of the intervals(c) the cumulative frequencies(d) the arithmetic mean(e) the variance

27. A class has a mean grade of 65 with a variance of 4. You obtain a grade which correspondsto a standard score of -1. What is your grade?

A class has a mean grade of 70 with a standard deviation of 10. Your grade corresponds toa deviation score of 2. What is your grade?

28. The following are simple questions of probability:

a) In rolling a single die what is the probability of obtaining either a 4 or a 6?b) In drawing a card from a well shuffled deck, what is the probability of obtaining eitherking or a club?c) In rolling two dice what is the probability of obtaining either a 7 or an 11?d) In tossing a coin what is the probability of obtaining HHHHT in that order in five tosses?e) Given a well shuffled deck of 52 cards what is the probability in drawing four cards, ofdrawing an ace, king, queen and jack of the same suit in that order?

29. The following questions relate to the binomial distribution:

a) In tossing 5 coins what is the probability of obtaining 4 or more heads?b) In tossing 6 coins what is the probability of obtaining 4 or more heads?c) In tossing 10 coins what is the probability of obtaining no heads?d) In rolling three dice what is the probability of obtaining no sixes?


9/12

30. Write down the expected distribution of heads in tossing six coins 64 times. What is themean and standard deviation of this distribution?

31. Assume that the distribution of Intelligence Quotients is normally distributed with a mean of100 and a standard deviation of 15 What proportion of people might be expected to haveIQs (a) above 115, (b) below 130, (c) between 90 and 110, (d) between 110 and 120, (e)either above 130 or below 120?

32. A variable is normally distributed with a mean of 100 and standard deviation of 20.

a) What percentage of the values is larger than 80?b) If 100 is added to every value, state the mean, median and standard deviation of this newvariable.c) If every value is multiplied by -2, state the mean and standard deviation of the newvariable.d) If random samples of size N = 4 were drawn from the original population, what would bethe mean and standard deviation of the distribution of sample means?

33. The following are data for scores for a sample of males and a sample of females on the sametest:

Males Females

" 50 60s 10 15N 100 200

Test to see whether males and females differ.

34. Use the normal distribution to approximate the probability of obtaining 15 or more heads on

tossing 50 unbiased coins.

35. The following are paired observation on number of mistakes (X) and number of practicetrials (Y).

X 1 2 3 4 5Y 2 1 4 3 5

Test to see if there is a significant relationship between # of mistakes and # of trials.

36. Consider a small population of numbers from 1 to 5. Write down the theoretical samplingdistribution of means of samples of size 3. Note that there are 10 equally probable samples.

37. Error scores on a learning task for nine rats who have taken alcohol are 13, 12, 11, 11, 11, 9,8, 8, and 7. The scores for three rats who have not taken alcohol are 8, 5, and 5. Higherscores reflect less learning. Perform a test of significance of the difference between themeans of the two groups, to determine if alcohol impairs learning.


10/12

38. Given the following observations representing the number of errors made by 5 studentsbefore and after a conference

Before 12 13 15 16 19 " B= 15.0After 8 10 5 9 8 " A= 8.0

Did the number of errors decrease?

39. Below are the scores for 5 students on 2 class tests

Test 1 1 2 4 5 8Test 2 8 5 1 2 4

Test to see if a significant relationship between the scores on the 2 tests exists. Comment.

40. A class of 100 students obtains a mean test score of 75 with a variance of 25. Can you show

that they performed significantly better than the (population) average of 65?

41. Four coins are tossed 64 times resulting in the following distribution of heads. Can youshow that the coins are biased?

Heads f

4 03 20

2 281 160 0

42. An experiment was done in which subjects were asked to indicate their preference for thearomas of two brands of coffee. When the judgments were classified according to the sex ofthe subject and the brand of coffee, the following table was obtained:

Coffee

Sex Brand A Brand BMale 9 21Female 29 21

Do the sexes differ in their choice of coffee brand?

43. A test has a standard deviation of 15 when a group of twenty women is tested and has astandard deviation of 10 when a group of twenty men is tested. How would you go aboutfinding out if men are less variable than women?


11/12

44. Is there a significant association between study time and grade?

Study Time

More than Average Average Less than Average

Pass 15 12 3 30

GradeFail 5 8 17 30

20 20 20

How many degrees of freedom are associated with the test statistic?

45. The following table shows the dominant hand and eye for each of 20 subjects

Eye

Right Left

Right 7 1 8Hand Left 1 7 8

Ambidextrous 2 2 4

10 10 20

Is there a significant association between the two dominances?

46. A 20-point midterm test results in grades which are normally distributed with a mean of 13 andstandard deviation of 3. The professor has decided that 15% of the class will get As, 30% will geBs, 30% will get Cs, 15% will get Ds and 10% Fs. What would be the minimum and maximumscores required for each of these grades?

47. You want to call a friend on the phone. You remember the first 3 digits of the phone number buhave no recollection of the last 4 digits. Whats the probability of getting the right number just by

guessing? What would the probability be if you knew that each of the 7 numbers occurred jusonce?

48. A student is taking a multiple choice exam with 5 possible answers for each question. If thestudent guesses (completely at random) on 32 questions, what is the probability that shell get 18or more of them correct?


12/12

49. A researcher investigates the relationship between smoking and illness. Tabled are the number ofcigarettes smoked per day and days absent from work over the past year.

a) Find the correlation between cigarettes smoked and days absent.b) Eliminate the data for the last 3 subjects and recalculate r. What effect have you found and howwould you explain it?c) In each case, what percent of the variance have you explained? Of what use is this value?

Cigarettes Smoked Days Absent

0 10 30 8

10 1013 220 1427 235 635 1244 1653 10

60 16

50. The new psychology course evaluation, in a class of 150 students, asks each student to report howmany hours a week they study. According to the responses, students average 15 hours a week witha standard deviation of 5 hours. Construct the 95% confidence interval for the population mean.

Documents

Exam Review Fall 2013