Download ASSIGNMENT 5 – DUE

ASSIGNMENT 4 – THE NORMAL DISTRIBUTION AND SAMPLING
Due Thursday, February 21
I will deduct points or refuse to accept assignments if they are disorganized and sloppy (e.g., presenting
answers out of order, illegible handwriting, loose papers, etc.).
Be sure to include all requested SPSS output. I would suggest pasting your SPSS output into Word and
entering your other answers where appropriate. You may hand-write answers to calculation problems, but
please keep the answers in order.
You must show your work to receive partial credit (1 point) for incorrect answers.
Staple your papers together and write your name at the top. Keep a copy for yourself just in case.
Problems
1. Use the frequencies procedure in SPSS to create a frequency distribution and histogram with a superimposed
normal curve and to calculate the mean, median, and standard deviation for TVHOURS [in the GSS08PFP-B
data file]. Hint: Once the data are open, select Analyze, Descriptive Statistics, and Frequencies. Move the
variable into the “Variable(s):” box. Click on the Statistics box and select Mean, Median, and Standard
Deviation. Click on the Charts box and select Histogram with Normal Curve.
a. Present the SPSS output including the mean, median, standard deviation, frequency distribution, and
histogram with the normal curve. [2 points]
b. Assuming that the distribution is normal (it may not be), what percentage of respondents should have a value
of less than 3.02? [2 points]. Note: 3.02 is the mean value. You don’t need to look this answer up in the table,
you should know it based on understanding the normal distribution.
c. Based on your SPSS output, what percentage of respondents actually has a value of less than 3.02? [2 points]
Include 3.0 in your calculation.
d. Does the empirical distribution of TVHOURS deviate from the theoretical normal curve (yes or no)?
[2 points]
2. A social psychologist has developed a test to measure racial prejudice. The test is normed so that it has a
mean of 75 and standard deviation of 15, and the prejudice scores are normally distributed in the population of
college students used to develop the test. You must show your work to receive full credit.
a. What is the percentile rank for a score of 58 (i.e., what percentage of scores fall below a score of 58)?
[2 points]
b. What percentage of scores falls between 52 and 65? [2 points]
c. What is the standard score (i.e., the z score) for a prejudice score of 72? [2 points]
d. What proportion of students should score above 87? [2 points]
e. What is the cutoff score (i.e., the prejudice score) below which 75 percent of all scores fall? [2 points]
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3. The number of hours people work each week varies widely for many reasons. Suppose you found that the
mean number of hours worked last week was 40.5 with a standard deviation of 13.2 hours, based on a sample of
1,575 individuals. You must show your work to receive full credit.
a. Assume that hours worked is normally distributed. What is the probability (remember that probabilities are
proportions) that someone will work more than 50 hours in a week? [2 points]
b. How many people in the sample should work more than 50 hours in a week? [2 points]
c. What is the probability that someone will work less than 30 hours in a week? [2 points]
d. How many people in the sample should work less than 30 hours in a week? [2 points]
4. A lower-level sociology class at a large urban university has 160 students, including 27 seniors, 33 juniors,
41 sophomores, and 59 freshmen. You must show your work to receive full credit.
a. Imagine that you choose one random student from the classroom. What is the probability that the student will
be a junior? [2 points]
b. What is the probability that the student will be a freshman? [2 points]
c. If you are asked to select a proportionate stratified sample of size 40 from the classroom, stratified by class
level (i.e., senior, junior, etc.), how many students from each group will be in the sample? [4 points, 1 for each
class level] Hint: please round to the nearest student.
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