9.6 A random sample tends not to be an exact replica of its parent population.
This fact has a number of implications. Indicate which are true and which are false.
a) All possible random samples can include a few samples that are exact replicas of the population, but most samples aren’t exact replicas.
b) A more representative sample can be obtained by handpicking (rather than randomly selecting) observations.
c) Insofar as it misrepresents the parent population, a random sample can cause an erroneous generalization.
d) In practice, the mean of a single random sample is evaluated relative to the variability of means for all possible random samples.
9.7 Define the sampling distribution of the mean.
9.8 Specify three important properties of the sampling distribution of the mean.
9.9 If we took a random sample of 35 subjects from some population, the associated sampling distribution of the mean would have the following properties (true of false)
a) Shape would approximate a normal curve.
b) Mean would equal the one sample mean.
c) Shape would approximate the shape of the population.
d) Compared to the population variability would be reduced by a factor equal to the square root of 35.
e) Mean would equal the population mean.
f) Variability would equal the population variability.
9.10 Indicate whether the following statements are true of false. The sampling distribution of the mean.
a) is always constructed from scratch, even when the population is large.
b) serves as a bridge to aid generalizations from a sample to a population.
c) is the same as the sample.
d) always reflects the shape of the underlying population.
e) has a mean that always coincides with the population mean.
f) is a device used to determine the effect of variability, that is, what can happen, just by change, when samples are random.
g) remains unchanged even with shifts to a new population or sample size.
h) supplies a spectrum of possibilities against which to evaluate the one observed sample mean.
i) tends to cluster more closely about the population mean with increases in sample size.
9.11 Someone claims that, since the mean of the sampling distribution equals the population mean, any single sample mean must also equal the population mean. Any comment?
9.12 Given that population standard deviation equals 24, how large must the sample size, n, be in order for the standard error to equal.
a) 8
b) 6
c) 3
d) 2
9.13 Given a sample size of 36, how large does the population standard deviation have to be in order for the standard error to be.
a) 1
b) 2
c) 5
d) 100
9.14 (a) A random sample of size 144 is taken from the local populations of grade-school children. Each child estimates the number of hours per week spent watching TV. At this point, what can be said about the sampling distribution?
b) Assume that a standard deviation, o, of 8 hours describes, the TV estimates for the local population of schoolchildren. At this point, what can be said about the sampling distribution?
c) Assume that a mean, m of 21 hours describes the TV estimates for the local population of schoolchildren. Now what can be said about the sampling distribution?
d) Roughly speaking, the sample means in the sampling distribution should deviate, on average, about_____hours from the mean of the sampling distribution and from the mean of the population.
e) About 95 percent of the sample means in this sampling distribution should be between_______ hours and ________hours.
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