Answer:
The margin of error for 90% confidence interval is 2.98, for 95% confidence interval is 3.55 and for 99% confidence interval is 4.68.
Step-by-step explanation:
The sample size is, <em>n</em> = 400.
The maximum value is, <em>Max.</em> = $225
The minimum value is, <em>Min</em>. = $80
The standard deviation of a distribution using the range of the data is:
As the sample is large, i.e. <em>n</em> = 400 > 30, according to the central limit theorem the sampling distribution of sample mean will follow a normal distribution.
The formula to compute the margin of error is:
- For a 90% confidence interval:
The value of <em>α</em> is 1 - 0.90 = 0.10
The critical value is,
(Use the standard normal table)
The MOE is:
- For a 95% confidence interval:
The value of <em>α</em> is 1 - 0.95 = 0.05
The critical value is,
(Use the standard normal table)
The MOE is:
- For a 99% confidence interval:
The value of <em>α</em> is 1 - 0.99 = 0.01
The critical value is,
(Use the standard normal table)
The MOE is:
Thus, the margin of error for 90% confidence interval is 2.98, for 95% confidence interval is 3.55 and for 99% confidence interval is 4.68.