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AP Statistics
Confidence Intervals
1) Check to see if the following sample sizes are large enough to be approximated by a normal curve?
a) n = 50 & p = .3
e) n = 50 & p = .05
b) n = 15 & p = .45
f) n = 100 & p = .01
c) n = 100 & p = .7
g) n = 40 & p = .25
d) n = 60 & p = .25
h) n = 80 & p = .9
2) USA Today reported that 36% of adult drivers admit that they often or sometimes talk on a cell
phone when driving. This was based on a random sample of 1004 adult drivers. What is a 98%
confidence interval for the true proportion of adult drivers who have often or sometimes talk on a cell
phone when driving? (Do complete write-up)
3) A consumer group is interested in estimating the proportion of packages of ground beef sold at a
particular store that have an actual fat content exceeding the fat content stated on the label. How
many packages of ground beef should be tested to estimate this proportion to within .05 with 95%
confidence?
4) The Gallup Organization conducted a national study on crime victimizations and reports that 25% of
all households experience some sort of crime. In a random sample of 300 Plano households, 68 report
that they had experienced some sort of crime. Construct a 95% confidence interval for the true
proportion of Plano households that have experienced some sort of crime. (No full write-up, but check
sample size)
Based on this interval, is there evidence to suggest that the proportion of Plano households who
experienced some sort of crime is less than the national proportion?
AP Review – One Sample Inference
1) Which of the following is not true about constructing confidence intervals?
a) The value of the standard error is a function of the sample statistic.
b) The center of the confidence interval is the population parameter.
c) One of the values that affect the width of a confidence interval is the sample size.
d) If the value of the population parameter is known, it is irrelevant to calculate a confidence interval for it.
e) The value of the confidence level will affect the width of a confidence interval.
2) When determining sample size for a study dealing with a proportion, it is most conservative to use 0.5 as an
estimate of the sample proportion. Which of the following is the reason for this fact?
a) The study will focus only on two responses: success and failure.
b) 0.5 is the probability of flipping a coin. Since the survey deals only with a yes/no question, this probability
is appropriate.
c) 0.5 will produce the greatest standard error. Therefore, the sample size using this value will guarantee
that the margin of error for the study will be maximized.
d) This is a binomial probability situation in which n is a sample size, p = 0.5, and r is the number of positive
responses.
e) None of these explains the use of 0.5 for the calculation of the most conservative sample size.
3) A large company wants to find out what kinds of transportation its employees use to get to work. It conducts a
random survey of 55 employees, and 25 say they ride a bus. Construct a 95% confidence interval for the
proportion of employees who ride the bus to work.
a) (.32, .59)
d) (.41, .68)
b) (.34, .56)
e) (.43, .66)
c) (.28, .63)
4) Which of the following are true of the margin of error for a single population proportion?
I. Multiply the margin of error by z* to get the standard error.
II. The margin of error is a calculation that describes the error introduced into a study when the sample isn’t
truly random.
III. The margin of error describes a possible random sampling error that occurs within truly random samples.
a) I only
d) I and II only
b) II only
e) I and III only
c) III only
5) You want to estimate the proportion of people who experience computer crashes when they access a website.
Calculate the minimum sample size you would need to ensure a 4% margin of error for a 95% confidence interval.
a) 505
d) 1074
b) 601
e) 2401
c) 673
AP Review – z & t Intervals with Means
1) What is the critical value for a 96% confidence interval for a sample of size 20? ( 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) 
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 
 0.5 


a) 1.4  2.054
d) 1.4  2.183
 22 
 22 
 0.5 
 0.5 
b) 1.4  2.054
e) 1.4  2.189


22
 22 


 0.5 

c) 1.4  2.189
 22 
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.