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
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.