Inference variables:        n, sample size

                                        100(1-a )%, level of confidence

                                        s , population standard deviation (estimated by S)
 

Inferential Computed Values:     Width of confidence interval

                                                        Required n to meet error standards

                                                        Standard error of the mean, 
 

Answer should follow this outline:

1. Interpret the change in the inference variable

Remember you only change one of these three and keep the other two constant. Don’t confuse the issue in your explanation by changing more than one.

Example: If the population standard deviation, s , increases, then population values are further from the population mean, m . They are less homogenous (less similar).
 

2. Relate the impact of the change to the ease of obtaining a good estimate

Example: A larger population standard deviation (more dispersed population) means it will be hard to obtain a good estimate of the population mean, because the sample is more likely to include values that are further from (and unlike) the mean.
 

3. Relate the information in #2 that you just did to the inferential computed values. (Note: this most likely requires that you interpret the inferential computed value).

Examples: (1) The width of a 95% (or some other fixed level) confidence interval must increase to accommodate the increased difficulty of obtaining a good estimate and maintain the same level of confidence that the interval contains the true value.

(2) If the question is about the required n, then we would say that the sample size must increase to accommodate the increased difficulty of obtaining a good estimate and maintain the desired standards for the error bound (fixed level of confidence that error will not exceed the bound, B).
(3) The standard error of the mean, , which measures the dispersion of the  (sample means) about the population mean, m , must increase as more dispersed values in the samples push their means further from the population mean.