1. Cybil wanted to determine the toxicity of masculinity among Filipino men. To do this, she
wrote a quiz with 25 scale-type questions where, in each question, a respondent could give
a rating from 0 to 4 to express a certain level of agreement (or disagreement). These ratings
are then combined in order to obtain a composite toxic masculinity score. This composite
score ranges from 0 (least toxic) to 100 (most toxic).
She got a sample of 33 men working in managerial positions for manufacturing companies,
and asked each respondent to answer the quiz. The composite scores for the sample of men
are summarized in the following bar chart.
Toxic Masculinity Scores
12
Frequency
2
10
0
20-29
30-39
40-49
50-59
60-69
70-79
80-89
Score
a. Cybil wrote in her report: "Note that the frequency distribution of the sample of scores
is slightly skewed. Hence, the corresponding distribution of composite scores for the
whole population is not normally distributed." To her surprise, she was harshly
reprimanded for immediately declaring nonnormality based on her interpretation of
the visual summary. Explain why such a declaration should indeed be reprimanded.
b. Suppose that a hypothesis test will be performed to evaluate Cybil's statement. What
are the null and alternative hypotheses for this problem?
SS
c. Given your choices of null and alternative hypotheses, formulate the Type I and Type
Il errors. Try to use wordings that are appropriate for this specific problem.
(Hint: you can use the following format for each error - "Cybil assumes that
when in fact
.")
d. Use an appropriate statistical procedure to compare the frequency distribution
described by the bar chart to the following relative frequency distribution, which is
derived from an assumption of normality, and estimates for the population mean and
standard deviation. In your solution, explicitly state the name of the procedure, and
explicitly write an appropriate conclusion following from the result of the procedure.
quency
20 to 29 30 to 39 40 to 49
0.1094 0.1714 0.2467
50 to 59
0.2363
60 to 69 70 to 79 80 to 89
0.1506 0.0639 0.0217