Suppose That Instead of Having a Sample of 25 in Question

Question

Examlex · Accepted Answer

The Answer is If my sample size were 100, my standard error would be smaller (because larger samples should look more like the population, therefore reducing error). With a smaller standard error in the denominator of the formula for calculating a z score, I would end up with a larger z score. Larger z scores would be associated with smaller probabilities, so the chances of getting a sample mean of 11 when the population mean is 10 would be much smaller than .1056, if the sample was randomly selected and the n = 100. Here's what it would look like:

\sigma_{\bar{x}}

=

\frac{4}{\sqrt{100}}

= 4/10= .4
Now, to calculate my z score I go: z =

\frac{11-10}{.4}

\rightarrow

1/.4 = 2.5.
Area beyond z is 1 - .9938 = .0062.

Suppose That Instead of Having a Sample of 25 in Question

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