Question

If I wanted the margin of error for the 95% confidence interval to be 1 inch, I should select a simple random sample of size: (assume the population standard deviation = 2.415)

A. 5.
B. 7.
C. 23.
D. 39

Answer 1

To achieve a margin of error of 1 inch with a 95% confidence level, a simple random sample of size 5 should be selected.

Step-by-step explanation:

To determine the sample size required to achieve a margin of error of 1 inch with a 95% confidence level, we can use the formula:

sample size = (Z * σ) / E

where Z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and E is the desired margin of error.

In this case, the Z-score for a 95% confidence level is approximately 1.96 (rounded to two decimal places).

Plugging in the values, we have:

sample size = (1.96 * 2.415) / 1 = 4.74416

Rounding up to the nearest whole number, the required sample size is 5.

Answer 2

We are given with
Confidence interval of 95%. This corresponds to a Z value of 1.96
Margin of error, d = 1 inch
Population standard deviation, σ = 2.415 inch

We can calculate for the sample size using the formula
n = Z² σ² / d²
Substituting,
n = 1.96² (2.415)² / 1²
n = 22.4 ~ 23