Wayne State University Women Labor Force Questions

Sociology 210Winter 2023
Assignment 3 (due Friday, September 23 at 11:59pm submitted to Section Canvas.) Use three
significant figures (decimal places) when reporting answers that include decimals.
1 point bonus credit for submitting assignment on-time (not using extension)
1. 9 points. Returning to the Women’s Labor Force participation data from last week:
Iraq 11%
Syrian Arab Rep 16%
India
19%
Saudi Arabia 31%
Italy
40%
Bahrain 43%
Philippines 45%
Montenegro 48%
Nigeria 48%
Poland
48%
Domin. Repub 50%
Argentina 50%
Malaysia 51%
Spain
53%
Japan
53%
Portugal 53%
Russia 53%
Brunei
54%
Uruguay 55%
United States 56%
Jamaica 56%
Mali
58%
Israel
59%
Canada 61%
China 61%
Australia 62%
Peru 66%
Vietnam 70%
Ethiopia 72%
Nepal 80%
Madagascar 84%
Rwanda 86%
a) 4 points. Compute the range and inter-quartile range (can use either list or table method)
for this sample.
b) Using a formal test for outliers, list any data values that could be considered outliers. For
any that you find, (1) write the value down and (2) show on paper how you verified that it
can be considered an outlier. 5 points.
2. 8 points. A social psychologist interested in nonverbal communication decided to do an
informal study on eye contact. Knowing that eye contact tends to be associated with an
emotional connection, she believed that most people would be uncomfortable maintaining eye
contact for more than a few moments with a total stranger. To test this, she took a walk on a
crowded street and counted how many seconds she could maintain eye contact with various
strangers before they looked away. Her findings, in seconds, were: 3.5; 3.4; 2.8; 1.9; 1.5; 3.9;
2.7; 4.1; 1.9; 2.5; 4.3; 2.5; 5.7; 2.9; 2.1; 3.9; 3.1. Please treat these data as sample data (not
population). This matters for part b.
a) 3 points. Determine the mode, median, and mean for this data.
b) 5 points. Compute the variance and standard deviation for the sample data
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3. 12 points. Eighty students take a quiz that is worth 100 points. 10% of the students get 100
points, 40% get 90 points, 30% get 80 points, and 20% get 70 points. What is the mean score on
the quiz?
What is the standard deviation (treat the scores as population data)?
What is the interquartile range (IQR)? (Hint: create a frequency distribution table)
Twenty students who were not in the class that day later came in and took the quiz and two
scored 100, eight scored 90, six scored 70, three scored 50, and one scored 30. Would any of
these students’ scores be low enough to be considered outliers? Show your work.
4. 10 points. For a population with μ = 8 and σ = 0.75, 1 point for each solution,
a) Find the Z-score that corresponds with each of the following X values:
X = 8.25
X=0
X = 11
X=5
X=8
b) Find the raw score (X) for each of the following Z-scores:
Z = 1.5
Z = -0.333
Z=1
Z = -2.5
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Z = -8
5. 2 points. A distribution of raw scores, μ = 60. A beginner statistics student computes the Zscore associated with X = 50 and incorrectly finds that Z = 2.00. Based on what you know about
Z-scores, why must this Z-score be incorrect even without knowing the standard deviation?
(Answer can be stated in one sentence.)
6. 9 points. An instructor gives a quiz with a total of 25 points. The grading policy is such that
the scores are necessarily multiples of 5. She gets the following distribution:
Score
25
20
15
10
5
Percent of Class with score
50
20
15
10
5
a) 6 points. If there are 200 students in the course, what is the mean score and what is the
standard deviation (treat this as population data)?
b)
1 point. True of False. If this population data for 160 students instead of 200, but the
percentage of students who received each of the above scores remained the same, the
mean would remain the same, but the standard deviation would be different due to the
smaller number of scores in the population. (No calculation required.)
c) 2 points. If the quiz was given again to a different class with 300 students and the mean
and standard deviation were the same as found above in part a), do you have enough
information to compute the Z-score associated with a quiz score of 0? If yes, what is Z
when X = 0? If no, then what other information do you need to compute Z?
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