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AP Statistics
AP Review – Z and T Intervals with Means
1) What is the critical value for a 96% confidence interval for a sample
of size 20? (σ unknown)
a) 2.054
d) 2.205
b) 1.96
e) 2.093
c) 2.197
2) Which of the following statements is true?
a) A 95% confidence interval is narrower than a 90% confidence
interval for the same set of data.
b) Increasing the sample size will decrease the margin of error in
your confidence interval.
c) The critical value is the variance of the sampling distribution.
d) The point estimate is the measure of variation used in the
computation of the margin of error.
e) Smaller sample sizes produce larger margins of error because
smaller samples always have larger standard deviations.
3) Which of the following isn’t necessary to compute the sample size
appropriate for a given confidence level and margin of error?
a) x
d) m (the margin of error)
b) σ
e) All these values are necessary
c) z*
4) You compute a 99% confidence interval with sample size A and a
margin of error of  5 units. You now wish to compute a 90%
confidence interval with the same margin of error with a sample size
B. For this situation, which of the following is true?
a) B is greater than A
b) A is greater than B
c) A and B are equal
d) A must be twice as large as B
e) A equals the square root of B divided by the sample size
5) A sample of size 36 has s = 3 and yields the confidence interval
(23.5, 26.5). What is t*?
a) 0.5
d) 1.5
b) 1
e) Not enough information to
c) 3
answer
6) Which of the following is true?
I. In order to use t procedures, you must know the population
standard deviation.
II. t procedures are considered to be robust.
III. The standard error of the mean is an estimate of the
standard deviation of the sampling distribution of a sample
mean.
a) I only
b) II only
c) III only
d) I & II only
e) II and III only
7) El Burrito, a fast food chain, is attempting to standardize the process
in production of food items. It randomly selects 22 Grande Bean
Burritos from stores around the country and weighs them. The mean
weight is 1.4 pounds and the standard deviation is 0.5 pounds. Which
of the following is the correct procedure to calculate a 96% confidence
interval to estimate the true mean weight of the Grande Bean Burritos?
 0.5 

 22 
0.5 
b) 1.4  2.054

 22 
 0.5 

c) 1.4  2.189
 22 
a) 1.4  2.054
 0.5 

 22 
0.5 
e) 1.4  2.189

 22 
d) 1.4  2.183
8) A researcher computes a 90% confidence interval for the mean
weight (in pounds) of widgets produced at a factory. The interval is
(7.2, 8.9). Which of these is a correct interpretation of this interval?
a) Out of all the widgets produced in all widget factories, 90%
weigh between 7.2 and 8.9 pounds.
b) We can be 90% confident that all the widgets weigh between
7.2 and 8.9 pounds.
c) There’s a 90% chance the population mean is between 7.2 and
8.9 pounds.
d) Ninety percent of all sample means are equivalent to the true
mean weight of all widgets.
e) We are 90% confident that the true mean weight of widgets is
between 7.2 and 8.9 pounds.
9) A researcher is interested in estimating the mean blood alcohol
content of people arrested for driving under the influence. Based on
past data, the researcher assumes a population standard deviation of
0.065. What sample size is needed to estimate the true mean blood
alcohol content within .005 units at the 95% confidence level?
a) 25
d) 650
b) 26
e) Insufficient data to calculate
c) 649
10) Which of the following is a characteristic of the t distribution?
a) It contains a finite number of terms.
b) Its shape depends on the number of degrees of freedom.
c) It’s identical to the normal curve.
d) Its median is positive.
e) It can be used with a small sample size only if there are
outliers.
11) A group of dieters at a weight clinic are losing weight. Nine
patients have lost the following number of pounds in the past month:
26.2, 17.2, 13.6, 13.4, 12.8, 11, 9.9, 6.2, and 7.9. Find a 95%
confidence interval for the mean weight loss for the population of
dieters at this clinic.
a) (9.28, 16.99)
d) (8.92, 17.53)
b) (6.54, 19.73)
e) Insufficient data to calculate
c) (8.60, 17.67)
12) A teacher wants to estimate the mean difference between grades in
the fall and spring semesters of a specific course. The fall semester
averages were subtracted from the spring semester averages for each
student. A 95% confidence interval is (-1.013, 6.069). Which of the
following statements is true?
a) Since the confidence interval contains zero, we can say that
there is a significant mean difference between the grades in the
fall and spring semester.
b) Since the confidence interval contains zero, we cannot say that
there is a significant mean difference between the grades in the
fall and spring semester.
c) Since the confidence interval has more positive values, we can
say that there is a significant mean difference between the
grades in the fall and spring semester.
d) Since the confidence interval has some negative values, we can
say that there is a significant mean difference between the
grades in the fall and spring semester.
e) Since the confidence interval has some negative values, we
cannot say that there is a significant mean difference between
the grades in the fall and spring semester.
13) Which of the following statements is false?
a) A 95% confidence interval is narrower than a 90% confidence
interval for the same data set.
b) The sample mean, x , is called a point estimate of the
population mean.
c) Increasing the sample size will decrease the margin of error in
your confidence interval.
d) As the sample size increases, the critical value t* approaches
the critical value z* for any given confidence level.
e) For a t distribution, the degree of freedom is n-1.