ou receive a brochure from a large university The brochure i

ou receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than

3636

students. You want to test this claim. You randomly select

1818

classes taught by full-time faculty and determine the class size of each. The results are shown in the table below. At

alphaequals=0.100.10,

can you support the university\'s claim? Complete parts (a) through (d) below. Assume the population is normally distributed.

3939

3737

3434

3838

3838

3535

4949

3030

3333

4040

3535

5050

4242

4343

3535

3535

3030

2323

Solution

Set Up Hypothesis
Null,mean class size for full-time faculty is fewer than 36, H0: U<36
Alternate, H1: U>36
Test Statistic
Population Mean(U)=36
Sample X(Mean)=37
Standard Deviation(S.D)=6.526
Number (n)=18
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =37-36/(6.526/Sqrt(18))
to =0.65
| to | =0.65
Critical Value
The Value of |t | with n-1 = 17 d.f is 1.333
We got |to| =0.65 & | t | =1.333
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Right Tail - Ha : ( P > 0.6501 ) = 0.26215
Hence Value of P0.1 < 0.26215,Here We Do not Reject Ho

[ANSWERS]
We have evidence to support brochure indicates that the mean class size for
full-time faculty is fewer than 36