Name:
Test 4
Pts:
/50
1. In each of the following stories, identify the explanatory variable, the response variable, and the
statistical method used to determine whether there is a relationship between the two variables.
(a) A headline in USA Today proclaimed that ”men and women are equal talkers.” It referred to
a survey in which the number of words spoken in a particular day by each person in random
samples of 186 men and 210 women was recorded. The survey found that there was no significant
difference in the mean number of words spoken in a day by men and women.
Explanatory Variable:
Response Variable:
Inference Method (circle)
Two-sample t
ANOVA
Chi-square
(b) Campral is a drug used to help patients continue their abstinence from the use of alcohol. One
possible side effect from the use of Campral is an adverse reaction in the digestive system. A
clinical trial to determine whether this was in fact a side effect had three treatment groups: one
group received the normal dosage of campral, one group received a high dosage of campral, and
the third group received a placebo. It was determined that there was no significant difference
between these groups in terms of proportion of each group that had an adverse digestive reaction.
Explanatory Variable:
Response Variable:
Inference Method (circle)
Two-sample t
ANOVA
Chi-square
(c) Researchers compared the tar content of unfiltered cigarettes with that of filtered cigarettes
by testing a random sample of 100 of each and found a significant difference in the mean tar
content.
Explanatory Variable:
Response Variable:
Inference Method (circle)
Two-sample t
ANOVA
Chi-square
(d) There are six different colors of M&Ms. In order to test whether these is a difference in the
average weight of M&Ms by color, a large number of M&Ms of each color (chosen randomly)
are weighed and their average weight was computed. We found that there was no significant
difference in the average weight by color.
Explanatory Variable:
Response Variable:
Inference Method (circle)
Two-sample t
ANOVA
Chi-square
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2. Short answers!
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(a) Suppose that a statistical test determines that there is a difference in the response variable
between a control group and a treatment group. In order to infer that the treatment caused
the difference, we must know that
(b) Without knowing anything about the drug being tested and without seeing any data, what
seems wrong to you about the following conclusion?
There is a statistically significant difference (P = .41) in mean blood pressure reading
between the group taking quinapril and the control group (who received a placebo).
(c) There are a boatload of letters associated with the two-sample t test. Some of these are parameters and some are statistics. In the following list, circle those symbols that are parameters.
µ1
µ2
x̄1
x̄2
σ1
σ2
s1
s2
(d) ANOVA could be used in all situations that a two-sample t test is used to test the same
hypothesis. However we prefer the two-sample t test because it remains valid even if
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3. J.K. Rowling wrote Harry Potter and the Sorcerer’s Stone for children. On the other hand, Tolstoy’s
Was and Peace is a rather difficult book to read. The Flesch Reading Ease score is a number that is
supposed to measure the readability of a passage. Higher Flesch scores indicate writing that is easier
to read. Listed below are the Flesch scores of a random sample of 12 pages from each book.
Rowling 85.3 84.3 79.5 82.5 80.2 84.6 79.2 70.9 78.6 86.2 74.0 83.7
Tolstoy 69.4 64.2 71.4 71.6 68.5 51.9 72.2 74.4 52.8 58.4 65.4 73.6
Boxplots of these two distributions are below along with the output from a certain hypothesis test.
(a) What is the null hypothesis — in terms of the parameters — that is being tested?
(b) What is the conclusion of this hypothesis test? Be sure to state your conclusion in correct
statistical language and in the context of the data.
(c) The sample sizes are relatively small. Is there anything in the data to concern us about using
this particular hypothesis test?
(d) What is the name of the hypothesis test being done? (It is enough here to name the test
statistic.)
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4. If a light is flickering fast enough, we do not see it as flickering but rather as a continuous beam.
How fast does a light have to flicker before this happens? The critical flickering frequency (CFF,
measured in cycles per second) is the fastest rate of flickering that a person can detect. Different
individuals have a different CFF. A researcher wanted to know whether the CFF was related to a
persons eye color. He took a random sample of individuals and measured their CFF and recorded
their eye color (brown, green, blue). He then did the following analysis:
(a) What is the name of the statistical analysis being performed?
(b) What is the null hypothesis of this statistical test? Express your null hypothesis in terms of
parameters. Besides writing the hypothesis, explain clearly what the parameters are in terms
of the context of the data.
(c) What is the conclusion of the this analysis? Be sure to write your conclusion in correct statistical
language and in the context of the data.
(d) What is the name of the statistic computed in this test? (The column heading for that statistic
has been erased in the above output. The value of the statistic is 4.8.)
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5. A researcher was interested in whether the length of a driver’s commute is related to the size of the
car that he/she drives. A random sample of drivers from a certain city was taken and the size of
car and length of commute recorded for each. The lengths were short (less that 10 miles), medium
(between 10 and 20 miles) and long (more than 20 miles). The relevant contingency table is
(a) What is the null hypothesis being tested in this analysis? You may state the hypothesis in
words but you should be sure that it is in context.
(b) What is the conclusion of this analysis with respect to the null hypothesis? Be sure to write
your conclusion in correct statistical language and in the context of the data.
(c) What is the name of the statistic computed in this test?
(d) In the first box of the table is a number, 10.19, that is called the expected count. What does it
mean to say it is “expected”?
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