Stat 67 Practice Test 2
For each question, write the letter for the appropriate inference procedure. Then write the null and alternative
hypotheses for the appropriate inference test.
A) One sample z or t procedure for a mean
B) Matched pairs z or t procedure for a mean
C) Two sample (difference of means) z or t
procedure
1.
D) ANOVA
E) Regression and test of slope
F) Chi-square for two-way tables
G) One sample z procedure for a proportion
Can swimmers hold their breath longer than track-and-field athletes? A study recruited a random sample
of 27 swimmers and an independently selected random sample of 27 track-and-field athletes. Each
subject was asked to hold their breath as long as possible, and that length of time was recorded.
Letter:
H0:
H a:
2.
A pharmaceutical company makes aspirin tablets designed to weigh 5 grams (g) on average. To check that
this is true, a random sample of 100 tablets gives a mean tablet weight of 4.9 g with a standard deviation
of 0.5 g.
Letter:
H0:
H a:
3.
A study enrolled a cohort of 2073 adults suffering from diabetes. Participants were classified based on
whether they generally abstained from drinking alcohol, drank alcohol in moderation, or drank alcohol
frequently. At the end of the study, the researchers compared the rates of congestive heart failure in each
group to see if drinking habits might impact the risk of congestive heart failure in diabetic patients.
Letter:
H0:
H a:
4.
Letter:
H0:
H a:
A company manufactures a homeopathic drug that it claims can reduce the time it takes to recover from
jet lag after long-distance flights. A research group sets to test this claim. They recruit 40 adult volunteers
who take frequent trips from San Francisco to London and assign them to take a placebo for one of their
trips and the homeopathic drug for the other trip, in random order. The subjects are asked to record how
many days it takes them to recover from jet lag for each trip.
CHOICES:
A) One sample z or t procedure for a mean
B) Matched pairs z or t procedure for a mean
C) Two sample (difference of means) z or t
procedure
5.
D) ANOVA
E) Regression and test of slope
F) Chi-square for two-way tables
G) One sample z procedure for a proportion
A criminologist is studying crime in medium-sized cities. He has collected robbery rates and population
densities for 16 medium-sized cities and would like to find out if population density is related to robbery
rate.
Letter:
H0:
Ha:
6.
A study of the effect of antihistamines on driving ability was done using a driving simulator. Sixty
volunteer licensed drivers were randomly assigned to take either a sedating antihistamine, a non-sedating
antihistamine, or a placebo. The driving simulator was then used to record their breaking time, in
milliseconds, in reaction to an abrupt traffic jam.
Letter:
H0:
H a:
7.
A consumer magazine wants to see if there is a difference, on average, in the lifetime of two brands of
AAA batteries. The product testing department takes a random sample of 10 AAA batteries for each
brand and records the time (in hours) it takes to empty each battery when placed in continuous use to
light a small light bulb.
Letter:
H0:
H a:
8.
Letter:
H0:
H a:
A parenting book reported that 25% of teenage men spend more than 5 hours per day playing video
games. To verify the claim researchers surveyed 280 male high school students. Of the surveyed high
school students, 45 reported spending more than 5 hours per day playing video games.
9.
Companies often place advertisements to improve the image of their brand rather than to promote
specific products. Does the place where the advertisement is published influence brand perception? A
study randomly assigned business students to read a print advertisement about a fictitious company that
had a header either from “The Wall Street Journal” or from “The National Enquirer.” The students then
classified the company as trustworthly or not trustworthly.
Letter:
H0:
H a:
10. A pediatrician is concerned that many of her patients have high blood cholesterol levels. Eight patients
who just had routine blood work uncovering a high cholesterol level were randomly selected, and their
parents were asked to watch an educational video explaining the consequences of high blood cholesterol.
One month later, the patients’ blood cholesterol levels were measured again. Here are the findings:
Starting cholest.
212
219
210
217
204
211
209
223
Cholest. after 1 month
212
210
204
213
200
204
203
217
a)
Compute a 95% confidence interval for the true mean change in blood cholesterol after the educational
intervention in this population. Some values that might help you to do this more quickly are: sstarting=6.13,
safter 1 month=5.94, s1month-starting=2.66
b) What are the conditions for inference here, and are they met? Explain.
c)
From your confidence interval, can you conclude that the educational intervention significantly lowers
blood cholesterol levels in pediatric patients with high blood cholesterol levels? Explain.
11. The following (i-iv) are all real studies published in the last 3 years. Describe any problems with the study
design or conclusions. If there are no problems write "no problems". The following vocabulary words may
be useful to you:
a.
b.
c.
d.
e.
f.
g.
h.
no control group
correlation vs. causation
multiple comparisons
confounding
spurious correlation
failing to account for sampling variability
incorrect distribution/assumptions not met
statistical vs practical significance
i. At a conference on education, a professor reported an experiment about online
homework in her statistics class for college sophomores. In 2010, the students did not
have online homework and scored an average of 65\% on her final exam. In 2011, the
students did have online homework and scored an average of 75\% on her final exam.
She concluded that online homework helped the students learn (pvalue$<$ .05).
ii. In the Facebook study researchers deleted positive posts from a person's feed and
determined if he then posted fewer positive words. They had a sample size of N =
689,003. They reported, "When positive posts were reduced in the News Feed, the
percentage of positive words in people's status updates decreased by B = 0.1\%".
iii. Proceedings of the National Academy of Sciences published a recent study which said
"Feminine-named hurricanes (vs. masculine-named hurricanes) cause significantly more
deaths"
iv. Scientists study whether women are more likely to wear pink during their menstrual
periods. They test they following "Are women more likely to wear pink during their
menstrual period on cloudy days?" ,"Are women more likely to wear pink during their
menstrual period on sunny days?" ,"Are women more likely to wear pink during their
menstrual period on rainy days?" , and "Are women more likely to wear pink during
their menstrual period on clear but cold days?" They found that for cloudy days the p
value is less than 0.05 and publish saying "On cloudy days, women are significantly more
likely to wear pink during their menstrual periods".
12. One measure of diabetes control is glycolated hemoglobin (A1c). To assess the benefits of various types of
nutritional counseling on A1c levels, 21 patients were randomly divided into 3 groups: regular nutritional
counseling, intensive nutritional counseling, and nutritional counseling with goal setting. The change in
A1c level was recorded for each subject. Software output for the analysis is shown below.
Regular
Intensive
Goal setting
-3.5
-2.8
-2.1
-1.4
-0.7
A1c change
0.0
0.7
1.4
SUMMARY
Groups
Count
Sum
Average
Variance
Regular
Intensive
7
7
-7.6
-2.5
-1.0857
-0.3571
2.72809
1.21952
Goal Setting
7
-14.9
-2.1286
1.41905
Source of Variation
SS
df
MS
F
P-value
Between Groups
Within Groups
11.098
32.2
2
18
5.54905
1.78889
3.10195
0.06968
Total
43.298
20
ANOVA
a)
Are the conditions for the test met? Explain.
b) Write 1-2 sentences summarizing the results of the study.
13. In 1-3 sentences, explain which statistical problem the
cartoon is illustrating. (Cartoon is from xkcd.com)
Figure 1: t distribution table