Download Chapter 8 TEST REVIEW

AP Statistics Chapter 8 TEST REVIEW
Confidence Intervals – One Sample (Proportions and Means)
Name: ___________________________
Date: ____________________________
For the Chapter 8 Test, you need to know the following….
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Know how to interpret a confidence interval and confidence level. What key words must you include?
What key words should NOT be included in a confidence interval/level interpretation? (NO
PROBABILITY!)
Explain how a change in the sample size, standard deviation or confidence level affects the length of a
confidence interval.
Calculate standard errors for one sample proportions and one sample means.
Population Proportions Confidence Intervals:
 Know the conditions/assumptions to calculate a confidence interval for proportions – you need to know
them like the back of your hand!
 Find a z* value for any confidence level (for the calculation of a CI) using Table A or on your calculator.
For example, what z* corresponds to 92% confidence?
 Know the formula to calculate a confidence interval to estimate a population proportion (remember – it is
on the formula sheet but you need to be able to “piece it together.”
 Find the required sample size needed to obtain a specific margin of error (you need to know what makes
up the margin of error of a confidence interval – not on formula sheet!)
Population Means Confidence Intervals:
 Know the conditions/assumptions to calculate a confidence interval for means – you need to know these
like the back of your hand!
 Verify that the population is normal with boxplot and be sure to note the absence of outliers and strong
skewness (relates to the Normal assumption)
 Know when to use a z* critical value or a t* critical value for confidence intervals for population means
 Find t* value with either Table B or on your calculator.
 Know the formula to calculate a confidence interval to estimate a population mean (remember – it is on the
formula sheet but you need to be able to “piece it together.”
 Find the required sample size needed to obtain a specific margin of error (you need to know what makes
up the margin of error of a confidence interval – not on formula sheet!)
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Remember – PANIC!
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Let your calculator help you calculate the confidence intervals once you have it filled into the formula to
save time and common calculator input mistakes with square roots, parentheses, etc.
One-Sample Population Proportion CI: STAT →TESTS →1-PropZInt
One-Sample Population Means CI: STAT →TESTS →TInterval
Review Questions
1) A 2005 report by the American Management Association summarized the results of an extensive survey
given to 526 randomly selected U.S businesses. One of the questions asked was whether the company had
fired any employees for misuse of the Internet while at work. The report gave a 90% confidence interval for
.229 to .292 for the proportion of all U.S companies that have fired employes for misuse of the Internet while at
work.
(a) What proportion of the businesses in the sample has answered yes to this question?
(b) What is the margin of error?
(c) Interpret the confidence interval and the confidence level.
(d) Explain to someone who does not know anything about statistics why we can’t simply say that the
answer to part (s) is true for all U.S businesses?
2) Scores on the MATH SAT are believed to be normally distributed with mean 𝜇. The scores of a random
sample of three students who recently took the exam are 550, 620 and 480. A 95% confidence interval for 𝜇
based on these data is:
(A) 550.00 ± 173.90
(B) 550.00 ± 142.00
(C) 550.00 ± 128.58
(D) 550.00 ± 105.01
(E) 550.00 ± 79.21
3) You are told that the sample proportion of those who phoned in and answered YES is 𝑝̂ = 0.70 and the
standard error of the sample proportion is 0.0459. Determine the number of people who phoned in.
4) Other things being equal, the margin of error of a confidence interval increases as
(A) The sample size increases
(B) The sample mean increases
(C) The population standard deviation increases
(D) The confidence level decreases
(E) None of the above
5) A 95% confidence interval for the mean 𝜇 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 𝜇 is between 6 and 12
(B) 95% of values sampled are between 6 and 12
(C) If we took many, many additional random samples and from each computed a 95% confidence
interval for 𝜇, approximately 95% of these intervals would contain 𝜇.
(D) There is a 95% probability that the true mean is 9 and 95% chance that the true margin of error is 3.
(E) All of the above are true.
6) A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took
a random sample (assume it is an SRS) of 1200 registered voters and found that 620 would vote for the
Republican candidate. Let p represent the proportion of registered voters in the state that would vote for the
Republican candidate. A 90% confidence interval for p is:
(A) 0.517 ± 0.014
(B) 0.517 ± 0.022
(C) 0.517 ± 0.024
(D) 0.517 ± 0.028
(E) 0.517 ± 0.249
7) You want to compute a 96% confidence interval for a population mean. Assume that the population
standard deviation is known to be 10 and the sample size is 50. What is the critical value that is to be used in
calculating the confidence interval?
8) You want to compute a 90% confidence interval for the mean of a population with unknown population
standard deviation. The sample size is 30. What is the critical value that is to be used in calculating the
confidence interval?
9) 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 sample mean of the weighings is computed. Suppose the scale readings are
Normally distributed with unknown mean 𝜇 and standard deviation 𝜎 = 0.01𝑔. How large should n be so that
a 95% confidence interval for 𝜇 has a margin of error of ±0.0001?
(A)
(B)
(C)
(D)
(E)
100
196
27.061
10,000
38,416
10) Based on a survey of a random sample of 900 adults in the United States, a journalist reports that 60
percent of adults in the US are in favor of increasing the minimum hourly wage. If the reported percent has a
margin of error of 2.7 percentage points, what level of confidence was used?
--------------------------------------------------------------------------------------------------------------------------------------------------11) A random sample of 1100 teenagers (ages 12 to 17) was asked whether they played games online. 775 said
that they did.
(a) Construct and interpret a 99% confidence interval for the population proportion p.
(b) How large a sample would you need to take to estimate p within 2% at a confidence level?
12) Rocky Mountain Airlines Flight 441 flies from Denver to Albuquerque each day at 8:00am. The flight is
listed as taking 58 minutes, on average. A random sample of 9 of these flight times, rounded to the nearest
minute, is given in the table below.
56
62
59
58
60
57
59
61
62
(a) Construct a 95% confidence interval for the true mean flight time for Flight 441.
(b) Does the interval in (a) give you reason to suspect that the claim of 58 minutes is false? Explain.
(c) What concern do you have about the data used here to construct the confidence interval in part (a)?
Explain.