Question

College	Tuition	Number of Students
Washington University	$35,900	482
University of Washington	$16,579	1,179
Washington State	$16,000	832
Western Washington University	$8,038	27,389
Evergreen University	$6,400	8,676
Eastern University	$37,676	2,853
Peninsula College	$5,148	5,782
University of Oregon	$4,922	4,816
Portland State University	$5,180	5,457
Oregon State University	$5,777	9,406
Southern Oregon University	$4,483	1,697
Eastern Oregon University	$48,920	10,296
Western Oregon University	$5,407	13,809
University of Idaho	$9,480	141
Idaho State University	$21,212	2,834

Step 1: State the hypothesis and identify the claim. The average cost of college tuition is less than $9,550.00 per year as concluded from The College Board. At a=.025, can it be concluded that the average is less than $9,550.00 based on a sample of 15 colleges?

H0: mu>/=$9,550

H1: mu,$9,550 (claim)

Step 2: Find the critical value.

Step 3: Compute the sample test value.

Step 4: Make then decision to reject or not reject the null hypothesis.

Step 5: Summarize the results.

Answer 1

Given that,
population mean(u)=9550
sample mean, x =15408.1333
standard deviation, s =14334.8174
number (n)=15
null, Ho: μ=9550
alternate, H1: μ<9550
level of significance, alpha = 0.025
from standard normal table,left tailed t alpha/2 =2.145
since our test is left-tailed
reject Ho, if to < -2.145
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =15408.1333-9550/(14334.8174/sqrt(15))
to =1.583
| to | =1.583
critical value
the value of |t alpha| with n-1 = 14 d.f is 2.145
we got |to| =1.583 & | t alpha | =2.145
make decision
hence value of |to | < | t alpha | and here we do not reject Ho
p-value :left tail - Ha : ( p < 1.5828 ) = 0.9321
hence value of p0.025 < 0.9321,here we do not reject Ho
ANSWERS
---------------
null, Ho: μ=9550
alternate, H1: μ<9550
test statistic: 1.583
critical value: -2.145
decision: do not reject Ho
p-value: 0.9321
we do not have enough evidence to support the claim that average is less than $9,550.00 based on a sample of 15 colleges