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Transcript
```4/11/17
AP Statistics
Partner Activity Chapters 10, 11
Calculators are always allowed in AP Stats!
Statisticians:
1. A survey was conducted in which both men and women were asked a question about a current issue.
Possible responses to this question were “in favor of,” “not in favor of,” or “no opinion.” A chi-square
test is to be used to determine whether the response to this question is independent of gender. the
number of degrees of freedom for the chi-square test in this situation is
A. 6
B. 5
C. 3
D. 2
E. 1
2. Makers of a new pain-relieving medication claim that it relieves chronic pain faster than the current topselling pain reliever on the market. a double-blind experiment was conducted in which 10 people who
experience chronic pain were randomly selected to take either the new or the current medication. Each
of the 10 people recorded the time, in minutes, from taking the medication until pain relief. After an
appropriate time period, each of the 10 people took the other medication and recorded the time from
taking the medication until pain relief. The medication each person took first was randomly determined,
and because both medications look the same, the people in the study did not know which medication was
taken first. The table below shows summary statistics for the results.
Minutes until Pain Relief
New Medication
Mean
15.6000
Standard deviation
4.811
Difference
Current Medication (new – current)
16.025
-0.425
4.833
1.395
Which of the following is closest to the p-value of the appropriate test?
A. 0.1802
B. 0.3604
C. 0.4230
D. 0.5770
E. 0.8198
3. In an experiment testing whether a new feed increased mean weight gain when compared to an old feed,
it was found that the new feed gave a 10 kg bigger weight gain than the old feed. A two –sample t-test
with the proper one-sided alternative was done and the resulting p-value was 0.082. This means that:
A. There is an 8.2% chance the null hypothesis is true.
B. There was only an 8.2% chance of observing an increase greater than 10 kg, assuming the
null hypothesis was true.
C. There was only an 8.2% chance of observing an increase greater than 10 kg, assuming the
null hypothesis was false.
D. There is an 8.2% chance the alternate hypothesis is true.
E. There is only an 8.2% chance of getting a 10 kg weight increase.
4. An SRS of 25 male faculty members at a large university found that 10 felt that the university was
supportive of female and minority faculty. An independent SRS of 20 female faculty found that five felt
that the university was supportive of female and minority faculty. Let p1 represent the proportion of all
male faculty members at the university and p2 represent the proportion of all female faculty members at
the university who hold the stated opinion. A 95% confidence interval for p1 – p2 =
A. 0.15 0.355
B. 0.15 0.270
D. 0.15 0.138
C. 0.15 0.227
E. 0.15 0.168
5. The following two way table resulted from classifying each individual in a random sample of residents of
a small city according to level of education (with categories “earned at least a high school diploma” and
“did not earn a high school diploma”) and employment status (with categories “employed full time” and
“not employed full time”).
Earned at least a high school diploma
Did not earn a high school diploma
Total
Employed full time Not employed full time Total
52
40
92
30
35
65
82
75
157
If the null hypothesis of no association between level of education and employment status is true, which
of the following expressions gives the expected number who earned at least a high school diploma and
who are employed full time?
A.
(92)(52)
157
D.
B.
(92)(82)
157
(65)(52)
92
C.
E.
(82)(52)
157
(92)(52)
82
6. The manager of a factory wants to compare the mean number of units assembled per employee in a week
for two new assembly techniques. Two hundred employees from the factory are randomly selected and
each is randomly assigned to one of the two techniques. After teaching 100 employees one technique
one technique and 100 employees the other technique, the manager records the number of units each of
the employees assemble in one week. Which of the following would be the most appropriate inferential
statistical test in this situation?
A. one-sample z-test
B. two-sample t-test
D. chi-square goodness-of-fit test
C. paired t-test
E. one-sample t-test
7. A marketing research consultant for a hotel chain hypothesizes that men and women differ in their color
preference for guest rooms. The consultant shows pictures of rooms decorated with three different color
schemes to each person in a random sample of 110 men and to each person in a random sample of 90
women. The consultant asks each person to choose his or her favorite color scheme. A chi-square test
for homogeneity of proportions will be used to test the consultant’s hypothesis. Assuming that the
conditions for inference are met, which of the following statements is true for the test?
A. The null hypothesis for the test is that the proportion of each gender who prefer each color scheme is
1
.
3
B. The sample size is too small to detect a significant difference in a chi-square test for homogeneity of
proportions.
C. The test is not valid because the sample sizes are not equal.
D. The more that men and women differ in their color preferences, the larger the chi-square statistic will be.
E. The test would also be appropriate if 90 married couples had been used for the two samples.
8. (2014 #5 secure) The newspaper staff at a large high school randomly sampled students at the school to
investigate the relationship between choice of favorite sport to watch and gender. Students in the sample
Of the following five sports, which one is your favorite to watch:
baseball, basketball, football, gymnastics, or swimming?
The number of responses by choice of favorite sport to watch and gender were tabulated. The graph
below displays the relative frequencies of each sport by gender.
A. Write a few sentences summarizing what the graph reveals about the association between choice of
favorite sport to watch and gender for the students in the sample.
B. What statistical test should be used to investigate whether there is an association between choice of
favorite sport to watch and gender for the population of students at the high school? What is the
appropriate number of degrees of freedom the test should be based on?
C. The conditions for inference were determined to be satisfied, and the appropriate statistical test was
conducted. The value of the test statistic is 10.77. Is there convincing statistical evidence, at the
0.05 significance level, of an association between choice of favorite sport to watch and gender
for all students at the high school?
9. (2014 #3 secure) Patients exhibiting symptoms of a heart attack are routinely transported to a hospital in
an ambulance. In a study of a new treatment thought to reduce damage to the heart, patients
experiencing symptoms of a heart attack were randomly assigned to one of two groups. During
transportation to the hospital, patients in one group received standard care, and patients in the other group
received the new treatment consisting of standard care and the application of a blood pressure cuff.
The response variable measured for each patient was a number between 0 and 1, referred to as the
myocardial salvage index (MSI). A higher MSI value indicates a more positive outcome for the patient.
Summary statistics for the MSI responses of the two groups are shown in the table.
Do the data provide convincing statistical evidence that the new treatment results in a higher mean MSI
value than does the standard care among people similar to the patients in the study.
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