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CHAPTER 8 SECTION 4: CONTINUOUS PROBABILITY DISTRIBUTIONS
MULTIPLE CHOICE
170. Which of the following statements is false?
a. The chi-squared distribution is positively skewed.
b. All the values of the chi-squared distribution are non-negative.
c. The shape of the chi-squared distribution depends on its degrees of freedom.
d. All of these choices are true.
ANS: D
PTS: 1
REF: SECTION 8.4
171. Which of the following statements is correct regarding the percentile points of the F distribution?
a. F0.10,10,20 = 1/F0.90,10,20
b. F0.10,10,20 = 1/F0.10,20,10
c. F0.90,10,20 = 1/F0.90,20,10
d. F0.90,10,20 = 1/F0.10,20,10
ANS: D
PTS: 1
REF: SECTION 8.4
172. The Student t distribution:
a. is symmetrical.
b. approaches the normal distribution as the degrees of freedom increase.
c. has more area in the tails than the standard normal distribution does.
d. All of these choices are true.
ANS: D
PTS: 1
REF: SECTION 8.4
173. The Student t distribution with parameter v = 2 has a mean E(t) equal to:
a. 2
b. 1
c. 0
d. None of these choices.
ANS: C
PTS: 1
REF: SECTION 8.4
174. The Student t distribution with parameter v = 4 has a variance V(t) equal to:
a. 4
b. 0
c. 2
d. 1
ANS: C
PTS: 1
REF: SECTION 8.4
175. What number corresponds to t0.05,10?
a. 1.812
b. 1.372
c. 2.228
d. 1.833
ANS: A
PTS: 1
REF: SECTION 8.4
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copied, or distributed without the prior consent of the publisher.
176. If P(t > t.01,v) = 2.50, then the number of degrees of freedom v is:
a. 20
b. 21
c. 22
d. 23
ANS: D
PTS: 1
177. What number corresponds to
a. 28.30
b. 26.22
c. 21.00
d. 5.23
ANS: C
178. If
a.
b.
c.
d.
REF: SECTION 8.4
?
PTS: 1
REF: SECTION 8.4
, then the number of degrees of freedom v is:
5
6
7
8
ANS: B
PTS: 1
REF: SECTION 8.4
179. What number corresponds to F0.95,4,8?
a. 0.166
b. 6.040
c. 0.260
d. 3.840
ANS: A
PTS: 1
REF: SECTION 8.4
180. What number corresponds to F.025,3,5?
a. 14.88
b. 7.76
c. 12.06
d. 5.41
ANS: B
PTS: 1
REF: SECTION 8.4
181. Suppose X has a chi-squared distribution with 10 degrees of freedom. The mean of X is:
a. 10
b. 9
c. 20
d. None of these choices.
ANS: A
PTS: 1
REF: SECTION 8.4
182. Suppose X has a chi-squared distribution with 10 degrees of freedom. The variance of X is:
a. 10
b. 9
c. 20
d. None of these choices.
ANS: C
PTS: 1
REF: SECTION 8.4
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copied, or distributed without the prior consent of the publisher.
183. The number of parameters for an F distribution is:
a. 1
b. 2
c. 0
d. None of these choices.
ANS: B
PTS: 1
REF: SECTION 8.4
184. Suppose X has an F distribution. Which of the following is true?
a. f(x) is symmetrical.
b. All the values of X are non-negative.
c. The mean of X is zero.
d. All of these choices.
ANS: B
PTS: 1
REF: SECTION 8.4
185. Which of the following distributions can take on negative values?
a. Student t
b. 2
c. F
d. None of these choices.
ANS: A
PTS: 1
REF: SECTION 8.4
186. Which of the following distributions is not skewed?
a. Student t
b. 2
c. F
d. All of these distributions are skewed.
ANS: A
PTS: 1
REF: SECTION 8.4
187. Which of the following has a mean and variance that depend on degrees of freedom?
a. Student t
b. 2
c. F
d. All of these choices are true.
ANS: D
PTS: 1
REF: SECTION 8.4
TRUE/FALSE
188. The value of 2 with v degrees of freedom such that the area to its right under the chi-squared curve is
equal to A is denoted by
, while
denotes the value such that the area to its left is A.
ANS: T
PTS: 1
REF: SECTION 8.4
189. The variance of a Student t random variable with v degrees of freedom (v > 2) is always greater than 1.
ANS: T
PTS: 1
REF: SECTION 8.4
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copied, or distributed without the prior consent of the publisher.
190. Like that of the Student t distribution, the shape of the chi-squared distribution depends on its number
of degrees of freedom.
ANS: T
191. We define
PTS: 1
as the value of the F with v1 and v2 degrees of freedom such that the area to its right
under the F curve is A, while
ANS: T
REF: SECTION 8.4
PTS: 1
is defined as the value such that the area to its left is A.
REF: SECTION 8.4
192. The value of A such that P(A  t  A) = 0.95, where the degrees of freedom are 20, is 2.086.
ANS: T
PTS: 1
REF: SECTION 8.4
193. The variance of a 2 distribution is twice the value of its mean.
ANS: T
PTS: 1
REF: SECTION 8.4
194. As the degrees of freedom approach infinity, the values of a Student t distribution approach those of a
standard normal distribution.
ANS: T
PTS: 1
REF: SECTION 8.4
195. The value of an F distribution with v1 = 5 and v2 = 10 degrees of freedom such that the area to its left is
0.95 is 3.33.
ANS: T
PTS: 1
REF: SECTION 8.4
196. The expected value of the Student t distribution is zero.
ANS: T
PTS: 1
REF: SECTION 8.4
197. The variance of a Student t distribution approaches zero as the degrees of freedom approaches infinity.
ANS: F
PTS: 1
REF: SECTION 8.4
198. The value of an F distribution with v1 = 6 and v2 = 9 degrees of freedom such that the area to its right is
0.05 is 3.37.
ANS: T
PTS: 1
REF: SECTION 8.4
199. The value of a chi-squared distribution with 5 degrees of freedom such that the area to its left is 0.10 is
1.61.
ANS: T
PTS: 1
REF: SECTION 8.4
200. The Student t distribution looks similar in shape to a standard normal distribution, except it is not as
widely spread.
ANS: F
PTS: 1
REF: SECTION 8.4
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copied, or distributed without the prior consent of the publisher.
201. The value of a chi-squared distribution with 8 degrees of freedom such that the area to its left is 0.95 is
2.73.
ANS: F
PTS: 1
REF: SECTION 8.4
COMPLETION
202. The shape of the ____________________ distribution is similar to a normal distribution, except it has
more area in the tails.
ANS:
Student t
t
PTS: 1
REF: SECTION 8.4
203. The mean of a Student t distribution is ____________________.
ANS:
zero
0
PTS: 1
REF: SECTION 8.4
204. The variance of a Student t distribution approaches ____________________ as the degrees of freedom
increase to infinity.
ANS:
one
1
PTS: 1
REF: SECTION 8.4
205. A X2 distribution with 5 degrees of freedom has a mean of ____________________ and a variance of
____________________.
ANS:
5; 10
five; ten
PTS: 1
REF: SECTION 8.4
206. The mean and variance of a X2 distribution approach ____________________ as the degrees of
freedom increase.
ANS: infinity
PTS: 1
REF: SECTION 8.4
207. For values of degrees of freedom greater than 100, the X2 distribution can be approximated by a(n)
____________________ distribution.
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.
ANS: normal
PTS: 1
REF: SECTION 8.4
208. The shape of a X2 distribution is ____________________.
ANS:
positively skewed
skewed
PTS: 1
REF: SECTION 8.4
209. The F distribution has two parameters called degrees of freedom, 1 and 2. We call 1 the
____________________ degrees of freedom, and we call 2 the ____________________ degrees of
freedom.
ANS: numerator; denominator
PTS: 1
REF: SECTION 8.4
210. As the ____________________ degrees of freedom increase, the mean of the F distribution
approaches 1.
ANS: denominator
PTS: 1
REF: SECTION 8.4
211. The shape of an F distribution is ____________________.
ANS:
positively skewed
skewed
PTS: 1
REF: SECTION 8.4
SHORT ANSWER
212. Use the t-table to find the following values of t.
a. t.10,9
b. t.10,20
c. t.025,82
d. t.05,196
ANS:
a. 1.383
b. 1.325
c. 1.990
d. 1.653
PTS: 1
REF: SECTION 8.4
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copied, or distributed without the prior consent of the publisher.
213. Use the t-table to find the following probabilities.
a. P(t8 > 2.306)
b. P(t80 > 2.639)
c. P(t24 > 1.711)
d. P(t35 > 1.306)
ANS:
a. 0.025
b. 0.005
c. 0.050
d. 0.100
PTS: 1
REF: SECTION 8.4
214. Use the X2 table to find the following values of X2.
a.
b.
c.
d.
ANS:
a. 14.61
b. 37.6
c. 4.61
d. 45.44
PTS: 1
REF: SECTION 8.4
215. Use the X2 table to find the following probabilities.
a.
b.
c.
d.
ANS:
a. 0.900
b. 0.050
c. 0.025
d. 0.010
PTS: 1
REF: SECTION 8.4
216. Use the F table to find the following values of F.
a. F.01,12,20
b. F.05,20,40
c. F.025,5,15
d. F.01,8,30
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copied, or distributed without the prior consent of the publisher.
ANS:
a. 3.23
b. 1.84
c. 3.58
d. 3.17
PTS: 1
REF: SECTION 8.4
217. Use the F table to find the following values of F.
a. F.99,12,20
b. F.95,20,40
c. F.975,5,15
d. F.99,8,30
ANS:
a. 1 / 3.86 = 0.2591
b. 1 / 1.99 = 0.5025
c. 1 / 6.43 = 0.1555
d. 1 / 5.20 = 0.1923
PTS: 1
REF: SECTION 8.4
218. Use the F table to find the following probabilities.
a. P(F6,14 > 2.85)
b. P(F20,60 > 2.20)
c. P(F12,25 > 2.51)
d. P(F15,30 > 2.01)
ANS:
a. 0.05
b. 0.01
c. 0.025
d. 0.05
PTS: 1
REF: SECTION 8.4
219. Suppose you have a Student t distribution with 20 degrees of freedom.
a. Find the mean.
b. Find the variance.
c. Find the standard deviation.
ANS:
a. 0
b. 20/18 = 1.11
c. 1.05
PTS: 1
REF: SECTION 8.4
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copied, or distributed without the prior consent of the publisher.
220. Suppose you have a X2 distribution with 20 degrees of freedom.
a. Find the mean.
b. Find the variance.
c. Find the standard deviation.
ANS:
a. 20
b. 40
c. 6.32
PTS: 1
REF: SECTION 8.4
221. Suppose you have an F distribution with degrees of freedom 10, 20.
a. Find the mean
b. Find the variance.
c. Find the standard deviation.
ANS:
a. 20/18 = 1.11
b. [2(20)2 (10 + 20  2)] / [(10)(18)2 (20  4)] = 0.4321
c. 0.4321 = 0.6573
PTS: 1
REF: SECTION 8.4
222. What happens to the shape, mean, and variance of a Student t distribution as the degrees of freedom
increase?
ANS:
As the degrees of freedom of the Student t distribution increase, the shape approaches a standard
normal distribution; the mean remains 0; and the variance approaches 1.
PTS: 1
REF: SECTION 8.4
223. What happens to the shape, mean, and variance of a X2 distribution as the degrees of freedom increase?
ANS:
The shape becomes less positively skewed; the mean increases to infinity, as does the variance.
PTS: 1
REF: SECTION 8.4
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.