Question

College Tuition ~ A random sample of 65 two-year colleges in the United States found that the average tuition charged in 2008-2009 was $2,314.12 and a standard deviation of $1,184.68.

Note: Numbers are randomized in each instance of this question. Pay attention to the numbers in this question.

What is the upper bound for a 95% confidence interval for the actual mean tuition charged in 2008-2009? Give your answer to 4 decimal places.

Your Answer:

Answer 1

Given that,

$\bar x$ = $2314.12

s = $1184.68

n = 65

Degrees of freedom = df = n - 1 = 65 - 1 = 64

At 95% confidence level the t is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

t$\alpha$ ,df = t0.05,64 = 1.669

Margin of error = E = t$\alpha$,df * (s /$\sqrt$n)

= 1.669 * ( 1184.68/ $\sqrt$ 65)

= 245.2453

The 95% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

2314.12 - 245.2453 < $\mu$ < 2314.12 + 245.2453

2068.8747 < $\mu$ < 2559.3653

Upper bound = 2,559.3653