Name ____________________________________________________________________________
AP Statistics – Problem Set #10
There are 10 multiple choice and 1 “FRAPPY” on this problem set. Do all of your work within this packet. Circle the letter
corresponding to the best answer for the multiple choice questions (worth 1 point each). Answer the AP Free Response question
completely, but concisely (worth 4 points).
.
1.
The value of z* required for a 70% confidence interval is
(a)
(b)
(c)
(d)
(e)
(f)
2.
-0.5244
1.036
0.5244
0.6179
The answer can’t be determined from the information given.
None of the above. The answer is _____________________.
A 95% confidence interval for the mean  of a population is computed from a random sample and
found to be 9 ± 3. We may conclude that
(a) There is a 95% probability that  is between 6 and 12.
(b) There is a 95% probability that the true mean is 9 and a 95% chance the true margin of error is 3.
(c) If we took many, many additional random samples and from each computed a 95% confidence
interval for  , approximately 95% of these intervals would contain  .
(d) If we took many, many additional random samples and from each computed a 95% confidence
interval for  , 95% of them would cover the values from 6 to 12.
(e) All of the above.
3.
A 95% confidence interval for the mean reading achievement score for a population of third grade
students is (44.2, 54.2). Suppose you compute a 99% confidence interval using the same information.
Which of the following statements is correct?
(a)
(b)
(c)
(d)
(e)
The intervals have the same width.
The 99% interval is shorter.
The 99% interval is longer.
The answer can’t be determined from the information given.
None of the above. The answer is ______________________.
4.
To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is
repeatedly weighed a total of n times and the mean x of the weighings is computed. Suppose the scale
readings are normally distributed with unknown mean  and standard deviation
 = 0.01 g. How large should n be so that a 95% confidence interval for  has a margin of error of
± 0.0001?
(a)
(b)
(c)
(d)
(e)
5.
The Gallup Poll interviews 1600 people. Of these, 18% say that the jog regularly. The news report adds:
“The poll had a margin of error of plus or minus three percentage points at a 95% confidence level.” You
can safely conclude that:
(a)
(b)
(c)
(d)
(e)
6.
95% of all Gallup Poll sample like this one give answers within ± 3% of the true population value.
the percent of the population who jog is certain to be between 15% and 21%.
95% of the population jog between 15% and 21% of the time.
we can be 95% confident that the sample proportion is captured by the confidence interval.
if Gallup took many samples, 95% of them would find that 18% of the people in the sample jog.
The weights (in pounds) of three adult males are 160, 215, and 195. The standard error of the mean of
these three weights is
(a)
(b)
(c)
(d)
(e)
7.
100
196
27061
10000
38416
190
27.84
22.73
16.07
13.13
You want to compute a 90% confidence interval for the mean of a population with unknown population
standard deviation. The sample size is 30. The value of t* you would use for this interval is
(a)
(b)
(c)
(d)
(e)
1.645
1.699
1.697
1.96
2.045
8.
Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their
first year at a major university. The interval is to have a margin of error of $2. Based on last year’s book
sales, we estimate that the standard deviation of the amount spent will be close to $30. The number of
observations requires is closest to:
(a)
(b)
(c)
(d)
(e)
9.
25
30
608
609
865
In preparing to construct a one-sample t interval for a population mean, suppose we are not sure if the
population distribution is Normal. In which of the following circumstances would we NOT be safe
constructing the interval based on an SRS of size 24 from the population?
(a)
(b)
(c)
(d)
(e)
A stemplot of the data is roughly bell shaped.
A histogram of the data shows slight skewness.
A stemplot of the data has a large outlier.
The sample standard deviation is large.
The t procedures are robust, so it is always safe.
10. A Census Bureau report on the income of Americans says that with 90% confidence the median income
of all U.S. households in a recent year was $57,005 with a margin of error of ±$742, This means that
(a) 90% of all households has incomes in the range $57,005 ± $742.
(b) we can be sure that the median income for all households in the country lies in the range
$57,005 ± $742.
(c) 90% of the households in the sample interviewed by the Census Bureau had incomes in the range
$57,005 ± $742.
(d) the Census Bureau got the result $57,005 ± $742 using a method that will cover the true median
income 90% of the time when used repeatedly.
(e) 90% of all possible samples of this same size would result in a sample median that falls within
$742 of $57,005.