The National Center for Education surveyed 4400 college graduates about the lengths of time required to earn their bachelor's degrees. The sample mean is 5.15 years, and assume that standard deviation is known to be 1.68 years. Based on the sample data, construct the 99% confidence interval for the mean time required by all college graduates. Also determine the margin of error, E.

Formula using 99% confidence interval:

CI99 = mean ± [(2.58)(sd/√n)]

Note: Within the brackets is the margin of error.

Your data:

mean = 5.15
sd = 1.68
n = 4400

Plug the values into the formula and calculate.

I hope this will help get you started.

To construct the 99% confidence interval for the mean time required by all college graduates, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

First, let's calculate the standard error, which is the standard deviation of the sample mean:

Standard Error = Standard Deviation / √(sample size)

Given that the standard deviation is known to be 1.68 years and the sample size is 4400, we can calculate the standard error:

Standard Error = 1.68 / √4400 ≈ 0.025

The critical value is determined based on the desired confidence level. For a 99% confidence level, we need to find the critical value that corresponds to an alpha level of 0.01 (1% significance level) divided equally between the two tails of the distribution. Looking up the critical value in a standard normal distribution table or using statistical software, we find the critical value to be approximately ±2.576.

Now, we can construct the confidence interval:

Confidence Interval = sample mean ± (critical value * standard error)
= 5.15 ± (2.576 * 0.025)
= 5.15 ± 0.0644

Therefore, the 99% confidence interval for the mean time required by all college graduates is approximately (5.086, 5.214) years.

To determine the margin of error (E), we need to take half the width of the confidence interval:

Margin of Error (E) = (upper bound – lower bound) / 2
= (5.214 – 5.086) / 2
= 0.064 / 2
= 0.032

So, the margin of error is approximately 0.032 years.