A.) Creat a 90% confidence interval for the mean difference in cost. Be sure to

ID: 3147756 • Letter: A

Question

A.) Creat a 90% confidence interval for the mean difference in cost. Be sure to justify your procedure. Let each difference be equal to the nonresident tuition minus the resident tuition. B.) Interpret your interval in context. C.) A national magazine claims that public institutions charge state residents an average of $4100 less for tuition each semester. What does your confidence interval indicate about this assertion? (Round to the nearest cent as neaded) b) Interpret your intervail in context. Choose the correct answer below OA. For a samplee, 90% of eem wil have amaan deerence that fals within the oofdecenn pay, on averape, more than nesidents by a value between the lowe and upper bounda of the confdenoe internal With 90% O B. The caps lock

Explanation / Answer

Solution

Let X = tuition fee levied by colleges from non-resident students and Y = tuition fee levied by colleges from non-resident students.

Then, D = X – Y = excess fee levied from non-resident students.

We assume D ~ N(µ, 2).

We want to get 90% Confidence Interval (CI) for µ and use it to test the hypothesis that µ = 4100.

Back-up Theory

1) 100(1 - )% Confidence Interval for population mean is: {Xbar ± (s/n)(t/2)},

where Xbar = sample mean, s = sample standard deviation, n = sample size and t/2 = upper (/2)% point of t-distribution with degrees of freedom = n – 1.

2) If 100(1 - )% Confidence Interval for population mean does not contain 0, we reject the null hypothesis H0 : = 0.

Calculations

Confidence Interval:

From the given fee-data, the D-values, mean of D, Dbar, SD of D, s and other parameters are found to be as follows: (using Excel Functions)

0.1

n =

Xbar =

3500

s =

1633.7353

tn-1, /2 =

1.7959

90% CI for

3500 ± 846.9729

Lower Bound =

2653.0271

Upper Bound =

4346.9729

ANSWER

Interpretation

The above bounds imply that the mean difference can at the most 4346 and at the least2653. Or, put in a different way, there is just 10% chance that the mean difference will be more than 4346 or less than 2653. ANSWER

To test if mean difference is 4100:

Vide (2) of Back-up Theory, 4100 very much belong to the above CI, (2653, 4346). This implies that the hypothesis: Mean difference is 4100 is accepted. ANSWER

0.1

n =