Complete the following problems:
Text Book
Gravetter, F. J., & Wallnau, L. B. (2009). Statistics for the behavioral sciences (8th ed.). Belmont, CA: Wadsworth, Cengage Learning. (ISBN: 0495602205 or 9780495602200)
Kirkpatrick, L. A., & Feeney, B. C. (2009). A simple guide to SPSS for Windows for version 16.0 (9th ed.). Belmont, CA: Wadsworth, Cengage Learning. (ISBN: 9780495597667)
Q1. A researcher plans to compare two treatment conditions by measuring one sample in treatment 1 and a second sample in treatment 2. The researcher will then compare the scores for the two treatments. If the is a big difference between the two groups of scores,
a. Briefly explain how the difference may have been caused by the treatments.
b. Briefly explain how the difference simply may be sampling error.
Q2. Downs and Abwender (2002) found neurological deficits in soccer players who are routinely hit on the head with soccer balls with swimmers, who are also athletes but who are not regularly hit in the head. Is this an example of an experimental or nonexperimental study?
Q3. Four scales of measurement were introduced in this chapter: nominal, ordinal, interval, and ratio.
a. What additional information is obtained from measurements on an ordinal scale compared to measurements on a nominal scale?
b. What additional information is obtained from measurements on an interval scale compared to measurements on an ordinal scale?
c. What additional information is obtained from measurements on a ratio scale compared to measurements on an interval scale?
Q4. For the following scores, find the value of each expression:
X
6
1
3
4
2
a. ∑X =
b. ∑X2 =
c. ∑(X + 1) =
d. ∑(X + 1)2 =
Q5. Use summation notation to express each of the following calculations:
a. Add 1 point to each score, then add the resulting values.
b. Add 1 point to each score and square the result, then add the squared values.
c. Add the scores and square the sum, then subtract 3 points from the squared value.
Q6. Find the value requested for the distribution of scores in the following table.
X f
5 2
4 2
3 4
2 0
1 1
a. n =
b. ∑X =
c. ∑X2 =
Q7. For the following scores, the lowest value is X = 13. Place the scores in a frequency distribution table using
a. An interval width of 5.
b. An interval width of 10.
21 40 18 37 32 52 33 24 13
57 41 47 32 43 58 16 38 31
47 29 49 54 22 39 34 45 20
Q8. An instructor at the state college recorded the academic major for each student in a psychology class and obtained the following results:
Psych Bio Soc Engl Psych
Health Phys Ed Psych Art Psych
Soc Health Psych Phys Ed Soc
Hist Psych Art Health Psych
Nurs Soc Psych Psych Pol Sci
a. Construct a frequency distribution table for these data.
b. What type of graph would be appropriate to show the frequency distribution for these data?
Q9. The following frequency distribution presents a set of exam scores for a class of N = 20 students.
X f cf c%
90-99 4 20 100
80-89 7 16 80
70-79 4 9 45
60-69 3 5 25
50-59 2 2 10
a. Find the 30th percentile.
b. Find the 88th percentile.
c. What is the percentile rank for X = 77?
d. What is the percentile rank for X = 90?
Q10. Use a stem and leaf display to organize the following distribution of scores. Use 6 stems with each stem corresponding to a 10-point interval.
Scores: 16, 42, 53, 41, 69
34, 33, 40, 61, 23
53, 49, 55, 29, 10
44, 64, 51, 21, 39
36, 58, 60, 27, 47
14, 44, 38, 31, 56
Q11. Find the mean, median, and mode for the following set of scores
X f
10 2
9 3
8 5
7 6
6 3
5 1
Q12. A population of N = 10 scores has a mean of µ = 9. One score is removed from the sample and the new mean is found to be µ = 8. What is the value of the score that was removed? (Hint: Compare the values for ∑X before and after the score was removed.)
For all of the following situations, identify the measure of central tendency (mean, median, or mode) that would provide the best description of the "average" score:
a. A researcher asks each individual in a sample of 50 adults to name his/her favorite season (summer, fall, winter, spring).
b. An insurance company would like to determine how long people remain hospitalized after a routine appendectomy. The data from a large sample indicate that most people are released after 2 or 3 days but a few develop infections and stay in the hospital for weeks.
c. A teacher measures scores on a standardized reading test for a sample of children from middle-class, suburban elementary school.
Q13. One question on a student survey asks: in a typical week, how many times do you eat at fast food restaurant? The following frequency distribution table summarizes the results from a sample of n = 20 students,
Number of times per week f
5or more 2
4 2
3 3
2 6
1 4
0 3
a. Find the mode for this distribution.
b. Find the median for the distribution.
c. Explain why you cannot compute the mean number of times using the data in the table.
Q14. Does it ever seem to you that the weather is nice during the work week, but lousy on the weekend? Cerveny and Balling (1988) have confirmed that this is not your imagination-pollution accumulating during the work week most likely spoils the weekend weather for people on the Atlantic coast. Consider the following hypothetical data showing the daily amount of rainfall for 10 weeks during the summer.
Week Average Daily Rainfall on Weekdays (Mon.-Fri.) Average Daily Rainfall on Weekends (Sat.-Sun.)
1 1.2 1.5
2 0.6 2.0
3 0.0 1.8
4 1.6 1.5
5 0.8 2.2
6 2.1 2.4
7 0.2 0.8
8 0.9 1.6
9 1.1 1.2
10 1.4 1.7
a. Calculate the average daily rainfall (the mean) during the week and the average daily rainfall for the weekends.
b. Based on the two means, does there appear to be a pattern in the data?
Q15. Can SS ever have a value of less than zero? Explain your answer.
Q16. For the data in the following sample:
8, 1, 5, 1, 5
a. Find the mean and the standard deviation.
b. Now change the score of X = 8 to X = 18, and find the new mean and standard deviation.
c. Describe how one extreme score influences the mean and standard deviation.
Q17. For the following population of N = 10 scores:
14, 6, 8, 3, 13 8, 9, 12, 1, 6
a. Sketch a histogram showing the population distribution.
b. Locate the value of the population mean in your sketch, make an estimate of the standard deviation (as done in example 4.2).
c. Compute the SS, variance, and standard deviation for the population (how well does your estimate compare with the actual value of σ?).
Q18. For the following population of n = 7 scores:
12, 1, 10, 6, 3 3, 7
a. Sketch a histogram showing the sample distribution.
b. Locate the value of the sample mean in your sketch, make an estimate of the standard deviation (as done in example 4.5).
c. Compute the SS, variance, and standard deviation for the sample (how well does your estimate compare with the actual value of s?).
Q19. In an extensive study involving thousands of British children, Arden and Plomin (2006) found significantly higher variance in the intelligence scores for males than for females. Following are hypothetical data, similar to the results obtained in the study. Note that the scores are not regular IQ scores but have been standardized so that the entire sample has a mean of M = 10 and a standard deviation of s = 2.
a. Calculate the mean and the standard deviation for the sample of n = 8 females and for the sample n = 8 males.
b. Based on the means and the standard deviations, describe the differences in intelligence scores for males and females.
Female Male
9 8
11 10
10 11
13 12
8 6
9 10
11 14
9 9