Stats Survey Data – Population Proportion Z-Procedures
North Georgia Mathematics
Directions: Complete the correct z-procedure for each set of observed data below.
1. Type A gender difference? A recent survey tested for Type A personalities among 202
undergraduates at North Georgia. Of the 128 females, 11 had Type A personalities. Of the 74
males, 9 had Type A personalities. Test for a gender difference at the .1 level.
2. Texting and Driving. A recent survey asked UNG students to report how often they texted while
driving. Responses were “never,” “rarely,” “sometimes,” “often,” and “always.” Students were
categorized as “frequently” texting if they selected “often” or “always.” Test whether more than
15% of North Georgia students text frequently while driving at the .05 level given that 47 of 201
respondents did so.
3. Making Friends. A recent study asked UNG students whether they made friends most easily
with members of the opposite sex, same sex or either sex equally. Test at the .1 level whether
there is a gender difference for same sex friendships given that, in the survey, 17 of 61 males
and 22 of 114 females reported same sex friendships were the easiest for them to make.
4. Humor Styles. Research has shown a connection between naïve relationship beliefs and those
who have a Self-Defeating primary humor style. Estimate the percentage of UNG students who
have a Self-Defeating humor style using a 90% level of confidence given that 51 of 175 students
tested in a recent study where found to be primarily Self-Defeating with their humor.
5. Coping Humor. A strong sense of Coping Humor indicates a person who uses humor to relieve
stress and deal with the struggles of life. Test at the .05 level whether more than 10% of North
Georgia students exhibit strong Coping Humor. A recent study used a criteria of scoring 30 or
higher on the Coping Humor Scale to evaluate this criteria, and found that 21 of 175 North
Georgia students did so.
6. Facebook Friends. A recent study found that apporximately 40% of North Georgia students had
more than 800 friends on Facebook. For females invovled in Greek life, is this percentage
higher? Test the hypothesis at the .01 level given that 23 of 34 Greek females had more than
800 friends.
7. Gender differences for texting while driving? A recent survey asked UNG students to report
how often they texted while driving. Responses were “never,” “rarely,” “sometimes,” “often,”
and “always.” Students were categorized as “frequently” texting if they selected “often” or
“always.” For females, 22 of 109 “frequently” texted while driving. For males, 13 of 59
“frequently” texted while driving. Test for a gender difference at the .1 level.
8. Gender differences for texting while getting ready? A recent survey asked UNG students to
report how often they texted while getting ready in the morning. Responses were “never,”
“rarely,” “sometimes,” “often,” and “always.” Students were categorized as “frequently” texting
if they selected “often” or “always.” For females, 50 of 109 “frequently” texted while getting
ready. For males, 13 of 59 “frequently” texted while getting ready. Test for a gender difference
at the .05 level.
9. Being Perfect. Estimate the percentage of North Georgia students with highly perfectionistic
personalities given 31 of 186 students surveyed met the criteria in a recent survey. Use a 95%
level of confidence.
10. Naïve about Relationships. A recent research project used a score of 36 or higher on the Toxic
Relationships Beliefs Scale as a cutoff value to determine whether a student was particularly
naïve about relationships. Test for a gender difference in relationship naivite at the .05 level
given that 18 of 79 males and 16 of 135 females surveyed were found to be partically naïve.
Solutions
1. 2 Proportion Z-Test. Fails sample size verification (only 9 successes in male population). Data not
appropriate for z-procedures.
2. 1 Proportion Z-Test. Reject null: z = 3.57 and p = .0002
3. 2 Proportion Z-Test. Fail to reject null: z = 1.33 and p = .1837
4. 1 Proportion Z-Interval. Between 24.0% and 35.2%, margin of error = 5.6%
5. 1 Proportion Z-Test. Fail to reject null: z = 1.27 and p = .1019
6. 1 Proportion Z-Test. Reject null: z = 3.25 and p = .0006
7. 2 Proportion Z-Test. Fail to reject null: z = -.34 and p = .7335
8. 2 Proportion Z-Test. Reject null: z = 2.98 and p = .0029
9. 1 Proportion Z-Interval. Between 12.0% and 22.8%, margin of error = 5.4%
10. 2 Proportion Z-Test. Reject null: z = 2.12 and p = .0338