Question

LALCULATOR BLACK Chapter 8, Section 8.1, Question E22 If all other values remain constant, what happens to the width of a confidence interval a. as the sample size, n, increases? The width of the confidence interval b. as the level of confidence increases? The width of the confidence interval Click if you would like to Show Work for this question: Open Show Work SHOW HINT

Answer 1

Solution:

Width of confidence interval depends on margin of error E

Width = 2 X E

It is given by:

E = ếc X 3Vn

or

E = te x s/n

Part a) Sample Size n increases.

From above formula of margin of error, we can see , Margin of Error E is inversely proportional to  sample size n.

Thus as n increases , then margin of error E decreases.

Thus as margin of error E decreases, then width of confidence interval is also decreases.

Thus:

As Sample Size n increases, the width of confidence interval is decreases.

Part b) Level of confidence interval increases:

Values z_c or t_c depends on level of confidence , larger the confidence level, larger is the z or t critical value.

Margin of Error E is directly proportional to Z_c or t_c value.

Thus as Z_c or t_c value increases, Margin of Error E is also increases.

As Margin of Error E is also increases, the width of confidence interval is also increases.

Thus:

As Level of confidence interval increases, he width of confidence interval is increases.