Suppose that a simple random sample is taken from a normal population having a standard deviation of 14 for the purpose of obtaining a 95% confidence interval for the mean of the population. Complete parts(a) through(c) below.

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Part 1

a. If the sample size is 4, obtain the margin of error.

The margin of error for a sample size of 4 is

13.72.

(Round to two decimal places as needed.)

Part 2

b. Repeat part(a) for a sample size of 16.

The margin of error for a sample size of 16 is

enter your response here.

(Round to two decimal places as needed.)

Part 3

c. Can you guess the margin of error for a sample size of 64? Explain your reasoning.

The margin of error for a sample size of 64 is

enter your response here.

(Round to two decimal places as needed.)

Part 4

Explain your reasoning.

Because the sample size

increased

decreased

by a factor of

enter your response here from part(b) to part(c), the margin of error was

multiplied

divided

by

enter your response here.

(Type whole numbers.)