Download Ch09 Sect03 Keller MS AISE TB Last modified

CHAPTER 9 SECTION 3: SAMPLING DISTRIBUTIONS
MULTIPLE CHOICE
136. If two populations are normally distributed, the sampling distribution of the difference in the sample
means,
, is:
a. approximately normal for any sample sizes.
b. approximately normal if both sample sizes are large.
c. exactly normal for any sample sizes.
d. exactly normal only if both sample sizes are large.
ANS: C
PTS: 1
REF: SECTION 9.3
137. If two random samples of sizes n1 and n2 are selected independently from two populations with means
1 and 2, then the mean of
equals:
a. 1 + 2
b. 1  2
c. 1 / 2
d. 1 2
ANS: B
PTS: 1
REF: SECTION 9.3
138. If two random samples of sizes n1 and n2 are selected independently from two non-normally
distributed populations, then the sampling distribution of the sample mean difference,
, is
a. always non-normal
b. always normal
c. approximately normal only if n1 and n2 are both larger than or equal to 30
d. approximately normal regardless of n1 and n2
ANS: C
PTS: 1
REF: SECTION 9.3
139. If two random samples of sizes n1 and n2 are selected independently from two populations with
variances
and , then the standard error of the sampling distribution of the sample mean
difference,
a.
, equals:
b.
c.
d.
ANS: D
PTS: 1
REF: SECTION 9.3
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.
140. The standard deviation of
is also called the:
a. standard error of the difference between two sample means.
b. standard deviation of the difference between the population means.
c. normal approximation to the difference of two binomial random variables.
d. None of these choices.
ANS: A
PTS: 1
REF: SECTION 9.3
141. If two random samples of sizes 30 and 36 are selected independently from two populations with means
78 and 85, and standard deviations 12 and 15, respectively, then the standard error of the difference
and
is equal to:
a. 0.904
b. 3.324
c. 3.391
d. 0.833
ANS: B
PTS: 1
REF: SECTION 9.3
142. If two random samples of sizes 30 and 36 are selected independently from two populations with means
78 and 85, and standard deviations 12 and 15, respectively, then the mean of the difference
is
equal to:
a. 7
b. 7
c. (78  85) / (30  36) = 1.17
d. 78/30  85/36 = 0.24
ANS: A
PTS: 1
REF: SECTION 9.3
TRUE/FALSE
143. If two random samples of size 36 each are selected independently from two populations with variances
25 and 16, then the standard error of the sampling distribution of the sample mean difference,
,
is 5  4 = 1.
ANS: F
PTS: 1
REF: SECTION 9.3
144. If two random samples of sizes 30 and 32 are selected independently from two populations with means
121 and 109, then the mean of the sampling distribution of the sample mean difference,
,
equals 12.
ANS: T
PTS: 1
REF: SECTION 9.3
145. The expected value of the sampling distribution of
is
where i is the mean of
population i (i = 1, 2).
ANS: T
PTS: 1
REF: SECTION 9.3
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.
146. The standard error of the difference between sample means,
where
ANS: F
PTS: 1
, is calculated by the formula
is the variance of population i (i = 1, 2).
REF: SECTION 9.3
147. If two samples are selected independently from two non-normal populations, then the sampling
distribution of
is only approximately normal provided that either n1 or n2 is 30 or more.
ANS: F
PTS: 1
148. The standard error of the difference
ANS: T
PTS: 1
149. The mean of the difference
ANS: F
PTS: 1
REF: SECTION 9.3
is equal to the standard error of the difference
.
REF: SECTION 9.3
is equal to the mean of the difference
.
REF: SECTION 9.3
SHORT ANSWER
Professors' Salary
Suppose that the starting salaries of female math professors have a positively skewed distribution with
mean of $56,000 and a standard deviation of $12,000. The starting salaries of male math professors are
positively skewed with a mean of $50,000 and a standard deviation of $10,000. A random sample of
50 female math professors and a random sample of 40 male math professors are selected.
150. {Professors' Salary Narrative} What is the sampling distribution of the sample mean difference
? Explain.
ANS:
is normally distributed, since the original populations are normally distributed.
PTS: 1
REF: SECTION 9.3
TOP: STATISTICAL CONCEPTS & APPLIED QUESTIONS
151. {Professors' Salary Narrative} Find the expected value of the sample mean difference.
ANS:
E(
) = $6,000
PTS: 1
REF: SECTION 9.3
TOP: STATISTICAL CONCEPTS & APPLIED QUESTIONS
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.
152. {Professors' Salary Narrative} Find the standard error of the sample mean difference.
ANS:
= $2,319.483
PTS: 1
REF: SECTION 9.3
TOP: STATISTICAL CONCEPTS & APPLIED QUESTIONS
153. {Professors' Salary Narrative} What is the probability that the sample mean salary of male math
professors will not exceed that of the female math professors?
ANS:
0.9952 (approximately, by the Central Limit Theorem, since n is large enough)
PTS: 1
REF: SECTION 9.3
TOP: STATISTICAL CONCEPTS & APPLIED QUESTIONS
154. Two samples are selected independently from two normal populations and the mean and standard error
of the sampling distribution of
are 32 and 38.72, respectively. Calculate P(
> 0).
ANS:
P(
> 0) = P (Z > 0.83) = 0.7967
PTS: 1
REF: SECTION 9.3
TOP: STATISTICAL CONCEPTS & APPLIED QUESTIONS
155. Two random samples of sizes 30 and 36 are selected independently from two populations with means
80 and 88, and standard deviations 15 and 20, respectively.
a. Find the standard error of the difference between
and .
b. Find the probability that the mean of the first sample is smaller than the mean of the
second sample.
ANS:
a.
b.
= 4.314
P(
< 0) = P(Z < 1.85) = 0.9678 (by the Central Limit Theorem, since both sample
sizes are more than 30)
PTS: 1
REF: SECTION 9.3
TOP: STATISTICAL CONCEPTS & APPLIED QUESTIONS
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.
Worker Productivity
A factory worker productivity is normally distributed. One worker produces an average of 84 units per
day with a standard deviation of 24. Another worker produces at an average rate of 74 per day with a
standard deviation of 25.
156. {Worker Productivity Narrative} What is the probability that in any single day worker 1 will
outproduce worker 2?
ANS:
PTS: 1
REF: SECTION 9.3
TOP: STATISTICAL CONCEPTS & APPLIED QUESTIONS
157. {Worker Productivity Narrative} What is the probability that during one week (5 working days),
worker 1 will outproduce worker 2 on average?
ANS:
PTS: 1
REF: SECTION 9.3
TOP: STATISTICAL CONCEPTS & APPLIED QUESTIONS
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.