A) If 500 random samples were taken from a large population (n = 40 for each sam

Question

A) If 500 random samples were taken from a large population (n = 40 for each sample) and 95% confidence intervals were constructed around the mean of each of the 500 samples, how many of these confidence intervals, on average, would not contain the population mean?

B) Circle or underline the correct answers:  If you increased from .05 to .10 and kept sample size the same (n = 40), the size of the t or Z coefficient used to construct the confidence intervals would (increase / decrease), the width/length of the intervals would (increase / decrease) and the precision of the interval estimates would (increase/ decrease), relative to A).  Consequently, a (smaller/larger) number of the 500 confidence intervals would, by chance, notcontain the population mean, relative to A).

Explanation / Answer

a)

number of  confidence intervals, on average, would not contain the population mean =np=500*(1-0.95)

=25

b)

If you increased from .05 to .10 and kept sample size the same (n = 40), the size of the t or Z coefficient used to construct the confidence intervals would  decrease , the width/length of the intervals would decrease and the precision of the interval estimates would increase relative to A

Consequently, a larger number of the 500 confidence intervals would, by chance, notcontain the population mean, relative to A

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