Download 175 pounds x =

Name ________________________
AP Statistics
Date _____________
Schwimmer
Chapter 10 Review #1
Part I. Multiple Choice. Circle the number corresponding to the best answer.
1.
What is the critical value t* that satisfies the condition that the t distribution with 8 degrees of
freedom has probability 0.10 to the right of t*?
(1)
(2)
(3)
(4)
(5)
2.
1.397
1.282
2.89
0.90
None of the above. The answer is ____________________.
The government claims that students earn an average of $4500 during their summer break from
studies. A random sample of students gave a sample average of $3975, and a 95% confidence
interval was found to be $3525 < µ < $4425. This interval is interpreted to mean that
(1) if the study were to be repeated many times, there is a 95% probability that the true average
summer earnings is not $4500 as the government claims.
(2) because our specific confidence interval does not contain the value $4500 there is a 95%
probability that the true average summer earnings is not $4500.
(3) if we were to repeat our survey many times, then about 95% of all the confidence intervals
will contain the value $4500.
(4) if we repeat our survey many times, then about 95% of our confidence intervals will contain
the true value of the average earnings of students.
(5) there is a 95% probability that the true average earnings are between $3525 and $4425 for all
students.
3.
A 95% confidence interval for the mean reading achievement score for a population of thirdgrade students is (44.2, 54.2). Suppose you compute a 99% confidence interval using the same
information. Which of the following statements is correct?
(1)
(2)
(3)
(4)
(5)
4.
The intervals have the same width.
The 99% interval is shorter.
The 99% interval is longer.
The answer can’t be determined from the information given.
None of the above. The answer is ____________________.
The weights of 9 men have mean x = 175 pounds and standard deviation s = 15 pounds. What
is the standard error of the mean?
(1)
(2)
(3)
(4)
(5)
58.3
19.4
5
1.7
None of the above. The answer is ____________________.
5.
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 mean x of the weighings is computed. Suppose the
scale readings are Normally distributed with unknown mean µ and standard deviation
σ = 0.01 g. How large should n be so that a 95% confidence interval for µ has a margin of
error of ±0.0001?
(1)
(2)
(3)
(4)
(5)
6.
Suppose that the population of the scores of all high school seniors who took the SAT Math test
this year follows a Normal distribution with mean µ and standard deviation σ = 100. You read
a report that says, “on the basis of a simple random sample of 100 high school seniors that took
the SAT-M this year, a confidence interval for µ is 512.00 ± 25.76. ” The confidence level for
this interval is
(1)
(2)
(3)
(4)
(5)
7.
100
196
27,061
10,000
38,416
90%
95%
99%
99.5%
over 99.99%
The diameter of ball bearings is known to be Normally distributed with unknown mean and
variance. A random sample of size 25 gave a mean of 2.5 cm. The 95% confidence interval had
length 4 cm. Then,
(1)
(2)
(3)
(4)
(5)
the sample variance is 4.86.
the sample variance is 26.03.
the population variance is 4.84.
the population variance is 23.47.
the sample variance is 23.47.
Part II. Free Response. Communicate your thinking clearly. Answer completely, but be concise. Show
your work.
8.
An evaluator wishes to make a statement about the emotional maturity of the freshmen population
at a large high school, so she decides to choose a random sample of freshmen and administer an
emotional maturity test. How many students should she sample in order to be 99% confident that
her estimate of freshmen emotional maturity will be within 6 units of the true mean? (The test
publishers indicate that the population variance is 100 units).
9.
Crop researchers plant 15 plots with a new variety of corn. The yields in bushels per acre are:
138.0
109.6
139.1
127.3
113.0
115.6
132.5
130.4
140.7
130.2
109.7
111.7
118.9
105.5
134.8
Assume that σ = 10 bushels per acre.
(a) Find z* for a 99% confidence interval for the true mean µ of the population. Show your
work by drawing a sketch of the distribution and labeling all key numbers.
(b) Construct and interpret a 99% confidence interval for µ.
(c) Joey says that 99% of the observations are in this interval. Is Joey right? If not, what is the
proper interpretation of this 99% confidence interval?
10.
A steel mill’s milling machine produces steel rods that are supposed to be 5 cm in diameter.
When the machine is in statistical control, the rod diameters vary according to a Normal
distribution with mean µ = 5 cm. A large sample of 150 rods produced by the machine yields a
mean diameter of 5.005 cm and a standard deviation of 0.02 cm.
(a) Construct and interpret a 99% confidence interval for the true mean diameter of the rods
produced by the milling machine.
(b) Does the interval in (a) give you reason to suspect that the machine is not producing rods of
the correct diameter? Explain your reasoning.