Alex Weller
348
AP Stats Problems 11-15
11. 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”).
Employed Not employed
full time
full time
Earned at least a
high school diploma
Did not earn a high
school diploma
Total
Total
52
40
92
30
82
35
75
65
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?
92 52
157
92 82
B)
157
82 52
C)
92
65 52
D)
92
92 52
E)
82
A)
B. The expected value equals the Row Total times the Column Total, which is then
divided by the Table Total.
12. 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 and 100 employees the other
technique, the manger records the number of units each of the employees assembles in
one week. Which of the following would be the most appropriate inferential statistical
test in this situation?
A)
B)
C)
D)
E)
One-sample z-test
Two-sample t-test
Paired t-test
Chi-square goodness-of-fit test
One sample t-test
B. There are two independent samples and the population standard deviation is
unknown.
13. A random sample has been taken from a population. A statistician, using this sample,
needs to decide whether to construct a 90 percent confidence interval for the population
mean or a 95 percent confidence interval for the population mean. How will these
intervals differ?
A) The 90 percent confidence interval will not be as wide as the 95 percent
confidence interval.
B) The 90 percent confidence interval will be wider than the 95 percent confidence
interval.
C) Which interval is wider will depend on how large the sample is.
D) Which interval is wider will depend on whether the sample is unbiased.
E) Which interval is wider will depend on whether a z-statistic or a t-statistic is used.
A. The wider the interval, the more confident you are that the true mean is inside the
interval. So the higher the confidence level, the more confident you are.
Data set I
Data set II
_________________________
20
30 35
45 50
60
14. The boxplots shown above summarize two data sets, I and II. Based on the boxplots,
which of the following statements about these two data sets CANNOT be justified?
A) The range of data set I is equal to the range of data set II.
B) The interquartile range of data set I is equal to the interquartile range of data set
II.
C) The median of data set I is less than the median of data set II.
D) Data set I and data set II have the same number of data points.
E) About 75% of the values in data set II are greater than or equal to about 50% of
the values in data set I.
D. The lines on a boxplot are the first, second, and third quartiles, plus the maximum and
minimum numbers, not actual data points. The two data sets could have any number of
data points, but similar quartiles.
15. A high school statistics class wants to conduct a survey to determine what percentage
of students in the school would be willing to pay a fee for participating in after-school
activities. Twenty students are randomly selected from each of the freshman, sophomore,
junior, and senior classes to complete the survey. This plan is an example of which type
of sampling?
A)
B)
C)
D)
E)
Cluster
Convenience
Simple Random
Stratified Random
Systematic
D. The sample is randomly selected, but they are still in groups of freshmen, sophomores,
juniors, and seniors. That way, an overall conclusion can be made as well as individual
conclusions for each grade.