Show all relevant work; use the equation editor in Microsoft Word when necessary.(Statistics Experts)
9.7 Deﬁne the sampling distribution of the mean.(Statistics Experts)
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 or 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, the 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.
9.13 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) A random sample of size 144 is taken from the local population 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, (r, 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, µ, 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.
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