Question

A simple random sample of size 15 is drawn from a normal population whose standard deviation is assumed to be 8. What's the margin of error if you are going to construct a 95% confidence interval for the population mean?

A plus/minus 3.4

B. plus/minus 4.05

C. plus/minus 4.82

D. ± 5.33

E. plus/minus 1.05

Answer 1

B. plus/minus 4.05

The margin of error can be calculated using the formula:

Margin of Error = Z * (standard deviation / sqrt(sample size))

For a 95% confidence interval, the Z-value is 1.96. Given that the standard deviation is 8 and the sample size is 15, the margin of error would be:

Margin of Error = 1.96 * (8 / sqrt(15))
≈ 1.96 * 2.06265
≈ 4.05

Therefore, the margin of error would be plus/minus 4.05.