Part I. Multiple Choice. Clearly identify the best answer for each item below. You may record your responses on the exam form itself or in the blue book.

1.  A researcher wants to examine the relationship between family size and political attitudes for a group of 100 college students.  Students are asked to report the number of individuals in their immediate family and then complete an attitude questionnaire measuring political opinions. This study is best described as _______ research.

a)   experimental      b)   correlation       c)   quasi-experimental    d)   time series

2.  For an extremely skewed distribution of ratio scores, the best measure of central tendency would be the _______.

a)   mode      b)   median         c)   mean        d)   range

3. The standard error of the mean ( ) is an estimate of the _______.

a)   average distance between a sample mean and the population mean            

b)   the population standard deviation

c)   average distance between an observation and a sample mean                       d)   the size of the population

4.  Which of the following is an example of an operational definition?

a)   depression       b)   intelligence       c)   hunger      d)   heart rate

5.  A distribution of N = 10 scores has a m = 50 and s = 10.  If another five individuals, all with scores of X = 50, are added to this distribution, what will happen to the variability of the distribution?

a)   the variability will increase because you are increasing the size of the population

b)   the variability will decrease because more scores will be clustered around the mean

c)   the variability will remain the same

d)   cannot be determined from the information provided

6.  In a negatively skewed distribution of exam scores, Tom scored at the mean, Rita scored at the median, and Daryl scored at the mode. Who had the highest score?

a)   Tom        b)   Rita         c)   Daryl     d) cannot be determined

7.  A population of N = 25 scores is normally distributed with m  = 50 and s  = 10.  If all of the scores in this population are transformed into z-scores, the distribution of z-scores will have a mean of ____ and a standard deviation of ____.

a)   50 and 10                  b)   50 and 2                    c)   0 and 1                      d)   10 and 2                    e) cannot be determined 

8. Researchers compared the number of speech disfluencies (e.g., um, uh, er) uttered by professors in the disciplines of humanities, social sciences, and physical sciences. This would best be characterized as _______ research.

a)   experimental                          b)   correlation                           

c)   quasi-experimental                d)   time series

9.  If a set of raw scores is positively skewed, the set of z-scores derived from them will be ______.

a)   normally distributed                    c)   bell shaped but not symmetrical

b)   symmetrical but not normal        d)   positively skewed

10.  Each observation in a sampling distribution of the mean represents a(n) ______.

a)   individual raw score              d)   population mean

b)   sample mean                         e)   sample standard error

c)   deviation score

11. Which of the following is an example of a discrete variable?

a) number of miles run                     b) number of siblings      

c) time to complete a puzzle            d) age

12.  For a population with m = 30, if each score is multiplied by 4, the resulting population will have a mean of _____.

a)   30          b)   34          c)   60      d)   120

13. Larger samples (as compared to smaller samples) are more representative of the population from which they were selected.  This is because

a)   the SEM gets smaller as the sample size gets larger 

b)   the SEM gets smaller as sample size gets smaller

c)   sample means based on larger samples are more variable

d)   b and c 

14. A psychologist hypothesizes that the presence of others improves performance. To test this hypothesis, she provides participants with a set of 100 math problems and asks participants to solve as many of the problems as possible in a 30 minute time period. Participants are randomly assigned to work on the problems either in a room by themselves or in a room with three other participants. The psychologist records the number of problems each participant solves. In this study, the independent variable is

        a) the number of problems presented to participants

        b) the number of problems participants were able to solve

        c) whether the participant worked alone or in the presence of others

        d) whether or not performance improves

        e) this is not an experiment, so there is no independent variable

15.  Which of the following is an advantage of transforming X values to z-scores?

a)   all negative numbers are eliminated          

b)   the distribution will become normal in shape

c)   the precise location of a score can be determined

d)   all of the above

e)   all scores in the distribution move closer to the mean

16. A researcher measures the height (in inches) and weight (in pounds) of research participants. These values are then used to assign participants to one of three groups: underweight, normal, or overweight. These three groups represent a _____ measurement scale. Height and weight are measured on a _____ scale.

a) ordinal; ratio       b) nominal; ratio      c) ordinal; interval     d) nominal; interval

Part II. Please record all responses in the blue book. Show all work. Failure to show all work will result in loss of credit.

17.  A set of raw scores with m  = 78 and s  = 6 is converted to a set of transformed (standardized) scores with m  = 50 and s  = 10.  What is the transformed score for a raw score of 90?

18. The Central Limit Theorem states that the shape of the sampling distribution of the mean will be normal if one of two conditions is satisfied. Identify these two conditions.

19. A sample of 1000 registered voters provided the following information in a survey: political party affiliation, gender, and age. Based on the survey responses, there are 400 Republicans, 450 Democrats, and 150 Independents in the sample. Exactly half the respondents are male and half are female. Twenty-five percent of the sample is between the ages of 18–35, 55% of the sample is between the ages of 36–64, and the remaining respondents are aged 65 or older. Assume these three variables are independent.

(a) If you select one person at random from this sample, what is the probability that the person is a Democrat?

(b) If you select one person at random from this sample, what is the probability that the person is either male or between the ages of 36–64?

(c) If you select one person at random from this sample, what is the probability that the person is a female Republican aged 65 or older?

20. An educational psychologist asked a group of college students how many hours they study each day. These data are displayed in the following frequency distribution table. Complete the columns in the table and then answer the questions that follow. 

(a) How many students participated in this survey?

(b) What percentage of students reported studying 3 hours each day?

(c) What number of students reported studying 2 or fewer hours each day?

(d) What is the percentile rank for a value of 4.5 study hours?  

(e) A percentile rank of 70% is associated with how many hours?

(f) What is the mean number of study hours in this sample?

(g) What is the mode for this sample?

21. A sample of 5 psychology professors was asked to indicate the number of books they assign in their introductory psychology courses. Their responses were as follows:  2, 5, 8, 10, 15

(a) Compute SS (sum of squares) for these data.

(b) Compute the variance of these data.

(c) Compute the standard deviation for these data.

(d) Suppose that an additional 5 books were added to each value above. Would the standard deviation become larger, smaller, or stay the same?

(e) If the values above represented a population rather than just a sample of the population, would you obtain a larger, smaller, or the same value for the standard deviation? Explain.

22. Scores on the SAT are normally distributed with a mean of 500 and a standard deviation of 100.  

(a) What is the probability of randomly selecting a sample of 100 students with an average SAT score of 522 or greater?

(b) Approximately how much error is there between the mean for this sample and the population mean?

23. A psychologist tests participant’s sense of direction by leading each participant through a maze in the basement of the psychology building and then asking the participant to identify which of the four directions is north. In a sample of 100 participants, 32 correctly identified the direction. What is the probability that 32 or more people would correctly identify the direction if they were simply guessing?

24.  The amount of money that students spend on textbooks per semester is normally distributed with a mean of $275 and a standard deviation of $50. 

(a) What percent of students spend between $250 and $300 on textbooks?

(b) One particular student spent $400 on textbooks. What is this student’s percentile rank?

25. George and Jerry had their first psychology exam yesterday. The exam took George 75 minutes to complete, which corresponds to a z-score of –1.5. Jerry completed the exam in 90 minutes, which corresponds to a z-score of –0.5. Assuming the exam completion times were normally distributed, what was the mean and standard deviation for the population of exam times?