Question

Provide an example of

What happens to the confidence interval if you (a) increase the confidence level, (b) increase the sample size, or (c) increase the margin of error? Only consider one of these changes at a time. Explain your answer with words and by referencing the formula. .

Answer 1

The formula for the confidence interval for example for the mean is given by:

where the critical value corresponds to critical values associated to the Normal distribution. The critical values for the given α is and M.E is the margin of error.

a) Increase the confidence level, then the critical value will increase as well.

This will lead to the width of the confidence interval increasing.

b)

Increase the sample size n. From the above formula, n is inversely proportional to the confidence interval.

Increasing the sample size will decrease the width of the confidence interval,

c) Increasing the margin of error

It will again increase the width of the confidence interval.

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