Inferential Abstractions
Parameter Changes and Effects on Inferential Processes
Worksheet 21

1. Check on one line in each set of choices within parentheses to complete the logical consequences of a large population standard deviation on the required sample size, n.

a.     If the population standard deviation, s, is large, then population values are
        (__ widely dispersed,   __tightly clustered) about the population mean,
        (__m,  __).  In other words, we can say the population values are
        (__homogeneous,   __ nonhomogeneous).

b.     Hence, values in a sample from such a population are (__more,  __less)
        likely to be near the population mean.

c.     Consequently, sample means will be (__widely dispersed,  __tightly
        clustered) about the population mean.

d.    That is, estimating the population mean will be (__easy,  __difficult).

e.     Thus, in order to obtain a given level of confidence that the error bound is B
        when the population standard deviation is large, we require (__more, __less)
        information from the population in the form of (__more,  __fewer)
        (__observations,   __samples) than we would require when the population
        standard deviation is small.
 

2.     Check one box in each set of choices within parentheses to complete the
        logical consequences of a large confidence level (that the error bound of an
        estimate is B) on the required sample size, n.

a.     A large confidence level, 100(1-a)%, implies a (__large,  __small) chance
        that the bound on the error is indeed B.

b.    Alternatively, we could say that a large confidence level implies a (__large,
        ___small) risk that the error exceeds B.

c.     To accomplish this large confidence level requires that we obtain (__more,
        __less) information from the population when we estimate the population
        mean (__,  __m).

d.     It follows that to obtain this amount of information from the population, we
        will require (__more,  __fewer) (__observations,  __samples) than we
        would require when the confidence level is small.
 

3.     Why do we need to report and expect others making statistical inferences
        to report more than the sample mean when they estimate a population
        mean? What else should be listed in a thorough report of the inference
 
 

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