AP Statistics
Ch. 8 Review
Name ___________________________
Date _______________ Period ____
III. Anticipating patterns: exploring random phenomena using probability and simulation
D. Sampling distributions
7. t-distribution
IV. Statistical inference: estimating population parameters and testing hypotheses
A. Estimation (point estimators and confidence intervals)
1. Estimating population parameters and margins of error
2. Properties of point estimators, including unbiasedness and variability
3. Logic of confidence intervals, meaning of confidence level and confidence intervals, and properties of confidence intervals
4. Large-sample confidence interval for a proportion
1. You have measured the systolic blood pressure of a random sample of 25 employees of a company located near
you. A 95% confidence interval for the mean systolic blood pressure for the employees of this company is
(122, 138). Which of the following statements gives a valid interpretation of the confidence level?
(a) Ninety-five percent of the sample of employees have a systolic blood pressure between 122 and 138.
(b) Ninety-five percent of the population of employees have a systolic blood pressure between 122 and 138.
(c) If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the
population mean systolic blood pressure.
(d) The probability that the population mean blood pressure is between 122 and 138 is 0.95.
(e) If the procedure were repeated many times, 95% of the sample means would be between 122 and 138.
2. An analyst, using a random sample of n = 500 families, obtained a 90% confidence interval for mean monthly
family income for a large population: ($600, $800). If the analyst had used a 99% confidence level instead, the
confidence interval would be:
(a) Narrower and would involve a larger risk of being incorrect
(b) Wider and would involve a smaller risk of being incorrect
(c) Narrower and would involve a smaller risk of being incorrect
(d) Wider and would involve a larger risk of being incorrect
(e) Wider but it cannot be determined whether the risk of being incorrect would be larger or smaller
3. In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state
lottery. The standard error of the sample proportion is approximately
(a) 0.03
(b) 0.25
(c) 0.0094
(d) 6.12
(e) 0.06
4. In preparing to use a t procedure, suppose we were not sure if the population was Normal. In which of the following
circumstances would we not be safe using a t procedure?
(a)
A stemplot of the data is roughly bell-shaped.
(b)
A histogram of the data shows moderate skewness.
(c)
A stemplot of the data has a large outlier.
(d)
The sample standard deviation is large.
(e)
The t procedures are robust, so it is always safe.
5. Some scientists believe that a new drug would benefit about half of all people with a certain blood disorder. To
estimate the proportion of patients who would benefit from taking the drug, the scientists will administer it to a
random sample of patients who have the blood disorder. What sample size is needed so that the 95% confidence
interval will have a width of 0.06?
(a) 748
(b) 1068
(c) 150.
(d) 2056
(e) 2401
6. In a poll, (a) some people refused to answer questions, (b) people without telephones could not be in the sample,
and (c) some people never answered the phone in several calls. Which of these sources is included in the ±2%
margin of error announced for the poll?
(a) Only source (a).
(b) Only source (b).
(c) Only source (c).
(d) All three sources of error.
(e) None of these sources of error.
7. 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% z-confidence interval using the same information. What is the
interval?
8. Scores on a standard IQ test are normally distributed with a mean of 100 and a standard deviation of 10.
Determine the size of the sample required if a 90% confidence interval for the sample mean is 98 < x < 102.
9. In a certain large population, 40% of households have a total annual income of over $70,000. Determine the
size of the sample required if a 95% confidence interval for the sample proportion of households with an annual
income over $70,000 is 38% < p̂ < 42%.
10. The following scores come from a randomly selected sample of students
111
90
130
110
91
106
114
99
103
105
95
100
79
117
118
144
93
95
111
103
101
99
120
105
101
82
107
123
103
112
82
107
107
89
a. Find the mean and standard deviation of the set of scores interpreted as a SAMPLE.
b. Calculate a 95% confidence interval for μ, the mean score of all students who took the examination.
11. A sample of 25 seniors from a large metropolitan area school district had a mean score of x = 450 on the Math
SAT. Suppose we know that the standard deviation of the population of Math SAT scores for seniors in the
district is σ = 100. Assuming that the population of Math SAT scores for seniors in the district is approximately
normally distributed, find a 99% confidence interval for the mean Math SAT score for the population of seniors.
12. In a large department store, the customer’s waiting time to check out is thought to be approximately normally
distributed with a mean of 5.8 minutes and a standard deviation of 1.8 minutes. A customer got angry standing
in line and got a random sample of 32 customers waiting times. They are as follows:
5.3
5.4
6.8
5.3
6.3
8.1
3.9
8.9
8.2
4.7
4.6
7.6
6.6
7.1
5.2
6.5
7.7
9.8
7.4
4.8
3.6
5.9
4.0
8.9
9.0
5.5
5.8
5.9
5.1
6.1
6.7
8.0
Construct a 95% confidence interval. Does the customer have a right to be angry?