Download 25 MC 2 Sample Inference

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#25 AP Review – Mixed
AP Statistics
1) Which of the following is affected by outliers?
I. Mean
IV. Range
II. Median
V. Interquartile range
III. Standard deviation
a) I, III, and V
d) III and IV
b) II and IV
e) I, III, and IV
c) I and V
2) The longevity of people living in a certain locality has a standard deviation of
14 years. What is the mean longevity if 30% of the people live longer than 75
years? Assume a normal distribution for life spans.
a) 61.00
d) 82.35
b) 67.65
e) The mean cannot be determined
c) 74.48
from the information given.
3) Researchers randomly assign subjects to two groups, with each group
receiving a different asthma medication. For one month, researchers record the
number of asthma attacks suffered by each subject and compute the following
summary statistics.
x 1  3.8, s1  1.7, n1  23
x 2  4.2, s 2  1.5, n1  24
What are your test statistic, p-value, and conclusion for Ha: µ1 < µ2?
a) t = -.859, p = .8002, fail to reject H0
b) t = -.854, p = .1989, fail to reject H0
c) t = -.189, p = .1974, fail to reject H0
d) t = -1.823, p = .9590, fail to reject H0
e) t = -1.823, p = .0375, reject H0
4) A random sample of 20 batteries is tested and shows a mean life expectancy
of 218 hours with a standard deviation of 11 hours. Determine a 90%
confidence interval for the mean life expectancy of these batteries.
a) 218  0.95
d) 218  4.25
b) 218  3.27
e) 218  19.02
c) 218  4.05
5) According to one poll, 12% of the public favor legalizing all drugs. In a
random sample of six people, what is the probability that at least one person
favors drug legalization?
a) 0.380
d) 0.620
b) 0.464
e) 0.844
c) 0.536
6) Suppose you toss a fair die three times and it comes up an even number each
time. Which of the following statements is true?
a) By the law of large numbers, the next toss is more likely to be an odd
number than an even number.
b) Based on the properties of conditional probability the next toss is more
likely to be an even number given that three in a row have been even.
c) Dice actually do have memories, and thus the number that comes up on
the next toss will be influenced by the previous tosses.
d) The law of large numbers tells how many tosses will be necessary
before the percentages of evens and odds are again in balance.
e) The probability that the next toss will again be even is 0.5.
7) A study on school budget approval among people with different party
affiliations resulted in the following segmented bar chart:
100%
For
Against
50%
No Opinion
Dem
Rep
Ind
Which of the following is greatest?
a) Number of democrats who are for the proposed budget
b) Number of republicans who are against the budget
c) Number of independents who have no opinion on the budget
d) The above are all equal.
e) The answer is impossible to determine without additional information.
8) A company is interested in comparing the mean sales revenue per salesperson
at two different locations. The manager takes a random sample of 10
salespersons from each location independently and records the sales revenue
generated by each person during the last 4 weeks. He decides to use a t-test to
compare the mean sales revenue at the two locations. Which of the following
assumptions is necessary for the validity of the t-test?
a) The population variances at both locations are equal.
b) The population variances at both locations are not equal.
c) The population variances at both locations are known.
d) The population of the sales records at each location is normally
distributed.
e) The population of the difference in sales records computed by pairing
one salesperson form each location is normally distributed.
9) A manufacturer of ready-bake cake mixes is interested in designing a study to
test the effects of four different temperature levels (300, 325, 350, 375 degrees
F), two different types of pans (glass and metal), and 3 different types of ovens
(gas, electric, and microwave) on the texture of its cakes. How many different
treatment groups are used in this study?
a) 3
d) 20
b) 9
e) 24
c) 18
10) A research firm wants to determine whether there’s a difference in married
couples between what the husband earns and what the wife earns. The firm
takes a random sample of married couples and measures the annual salary of
each husband and wife. What procedure should the firm use to analyze the data
for the mean difference in salary within married couples?
a) One-sample t procedure, matched pair
b) Two-sample t procedure
c) One-sample z procedure, matched pair
d) Two-sample z procedure
e) Not enough information to determine which procedure should be used.
11) When you are estimating population means or doing hypothesis tests about
population means, when is it appropriate to use the t procedure?
a) When you are unsure about whether your sample is normally
distributed.
b) When you don’t know your population mean
c) When you don’t know your population standard deviation and your
sample is strongly skewed
d) When you don’t know your population standard deviation and your
sample shows no signs of extreme skewness or outliers
e) When you don’t know your sample size
12) Which of the following statements is true?
a) The sampling distribution of the difference between two proportions
will always be normal.
b) When comparing two population proportions, either sample proportion
can be used as the unbiased estimate of the true population proportion.
c) If sample sizes are large enough, and if the population is large compared
to the sample, we can compare two proportions using a normal
approximation.
d) When you’re doing inference for two proportions, then number of
degrees of freedom is one less than the smaller of the two sample sizes.
e) None of the above statements are true.
13) A backpack manufacturer wants to know if students in high school carry
more books than college students do. A random sample of 17 high school
students had a mean number of 3.647 textbooks with standard deviation of 1.9
books. A random sample of 17 college students reported a mean and standard
deviation of 2.529 and 1.7, respectively. Which of the following conclusions is
correct?
a) We have significant evidence to reject the null in favor of the alternative
hypothesis that high school students carry more books.
b) We don’t have significant evidence to reject the null in favor of the
alternative hypothesis that high school students carry more books.
c) We have significant evidence to support the conclusion that high school
students carry between 2.529 and 3.647 books.
d) We have significant evidence to support that there’s a difference between the
number of books high school and college students carry.
e) We don’t have significant evidence to support that there’s a difference
between the number of books high school and college students carry.
14) An engineer wishes to determine the mean amount of heat being generated
by a particular electronic component. If she knows that the population standard
deviation is 2.4, how many of these components should she sample to be 99%
sure of know the answer to within  0.6?
a) 27
d) 212
b) 87
e) 425
c) 107
15) A random sample of 384 people in Stats City revealed 112 individuals who
worked at more than one job. Another random sample of 432 workers from
Deviation Central found 91 people who work at more than one job. Find a 99%
confidence interval for the difference between the proportions of workers in the
two cities who work at more than one job.
a) (.003, .159)
d) (.031, .131)
b) (.021, .141)
e) Sample sizes are not large enough
c) (-.159, .004)
to use z-procedures
16) Which of the following statements are true?
I. When generating confidence intervals and doing significant tests for twosample proportions, we use the same expression for the standard error.
II. If zero is in the confidence interval for the difference between two
proportions, we have evidence that the two population proportions could be the
same.
III. When we do a significance test for the difference between two proportions,
we’re justified in pooling our estimates of the population proportion only if the
sample sizes are large.
a) I only
b) II only
c) III only
d) II & III
e) I & III
Answers:
1-E, 2-B, 3-B, 4-D, 5-C, 6-E, 7-D, 8-D, 9-E, 10-A, 11-D, 12-C, 13-A, 14-C,
15-A, 16-