Q 8.61 - Elementary Statistics

Question

Formula $8.2$ on page $327$ provides a method for computing the sample size required to obtain a confidence interval with a specified confidence level and margin of error. The number resulting from the formula should be rounded up to the nearest whole number.

a. Why do we want a whole number?

b. Why do we round up instead of down?

Step-by-Step Solution

Answer

a. We want a whole number as the sample cannot be in fraction.

b. This is due to the fact that margin of error is obtained from the smallest value of the sample size.

Step 1: Given Information

It is given that the number obtained from the formula rounded up to nearest whole number.

Step 2: a. Explanation of need of whole number

• We want a whole number as number of observation cannot be in fraction or part of member of population.
• Hence, number of observation should be a whole number.

Step 3: b. Why round up instead of down

• We round up instead of down because from the smallest value of sample size, required value of margin of error is obtained.
• Rounded up provide us number that is larger than the actual sample size.