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MATH 264 QUIZ # 5
December 26, 2002
ANSWERS
1) When we calculate a z-score in an application of the central limit theorem we use the
formula:
a) z =
x̄ − µ
σ
b) z =
x − µx̄
σx̄
c) z =
x̄ − µx̄
σx̄
"
d) z =
x−µ
σ
2) The standard deviation of the sampling distribution of x̄ is
deviation of the population.
a) greater than
c) equal to
the standard
b) greater than or equal to
d) less than
"
3) The mean weight of the students in a certain school is 80 k.g. and the standard deviation
is 5 k.g. The probability that the mean weight of a sample of 100 students is greater than 81
k.g. is: (Below F (z) denotes the area under the standard normal curve from 0 to z.)
a) 0.5 − F (2.5)
b) 0.5 + F (2)
c) 0.5 − F (2)
"
d) 0.5 + F (2.5)
4) When we sample from an infinite population, the standard error of the mean is multiplied
when we increase the sample size from 16 to 25
by a factor of
a)
16
25
b)
25
16
c)
4
5
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d)
5
4
5) Which of the following is true for the central limit theorem1 ?
a) It cannot be used if the population being sampled has a binomial distribution.
b) It can never be applied if n < 30.
c) It can be used for finite populations provided that n is small and n/N is large.
d) It can be used for finite populations provided that n is large and n/N is small.
"
6) A random sample of size 64 is selected from a population of size 100000 and standard
deviation is 5. The standard error of the mean is:
a)
64
20000
b)
20000
64
c)
8
5
d)
5
8
"
7) When the population being sampled has a normal distribution, the central limit theorem
can be applied:
a) for n ≥ 30
c) for n ≤ 0.05 · N
b) for n ≥ 0.05 · N
d) for any n
"
8) The probability of selecting a random sample of size 3 from a population of size 12 is:
a) 1/220
"
b) 1/1320
c) 220
d) 1320
9) It is impossible to apply the central limit theorem if the population does not follow a normal
distribution.
1 Here
and in what follows N denotes the population size.
TRUE
FALSE
"
10) In order to apply the central limit theorem, n must be larger if the population being
sampled has an unusual distribution.
TRUE
"
FALSE
11) A simple random sample from a finite population is a sample which is chosen in such a
way that each possible sample has the same probability of being selected.
TRUE
"
FALSE
12) The finite population correction factor is omitted in situations where n constitutes only a
small proportion of the population.
TRUE
"
FALSE
13) A sample can be either finite or infinite.
TRUE
FALSE
"
14) The standard deviation of the sampling distribution of the mean does not depend on the
sample size involved.
TRUE
FALSE
"
15) Sampling with replacement from a finite population is, in effect, sampling from an infinite
population.
TRUE
"
FALSE
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