Question

You want to estimate the difference between the average grades on a certain math exam before the students take the associated math class and after they take the associated math class. You take the random samples of 5 students who have taken the class and 5 students who have not taken the class. You get the following results:

Not Taken	Taken
54	82
25	76
73	98
23	43
42	38

A) Determine the population(s) and parameter(s) being discussed.

B) Determine which tool will help us find what we need (one sample z test, one sample t test, two sample t test, one sample z interval, one sample t interval, two sample t interval).

C) Check if the conditions for this tool hold.

D) Whether or not the conditions hold, use the tool you choose in part B. Use C=95% for all confidence intervals and alpha=5% for all significance tests.

* Be sure that all methods end with a sentence describing the results *

Answer 1

Given that,
null, H0: Ud = 0
alternate, H1: Ud != 0
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.776
since our test is two-tailed
reject Ho, if to < -2.776 OR if to > 2.776
we use Test Statistic
to= d/ (S/√n)
where
value of S^2 = [ ∑ di^2 – ( ∑ di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = 24
We have d = 24
pooled variance = calculate value of Sd= √S^2 = sqrt [ 4426-(120^2/5 ] / 4 = 19.66
to = d/ (S/√n) = 2.73
critical Value
the value of |t α| with n-1 = 4 d.f is 2.776
we got |t o| = 2.73 & |t α| =2.776
make Decision
hence Value of |to | < | t α | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 2.7297 ) = 0.0525
hence value of p0.05 < 0.0525,here we do not reject Ho
ANSWERS
---------------
A.
the difference between the average grades on a certain math exam before the students take the associated math class
and after they take the associated math class.
B.
Paired sample t test
C.
null, H0: Ud = 0
alternate, H1: Ud != 0
test statistic: 2.73
critical value: reject Ho, if to < -2.776 OR if to > 2.776
D.
decision: Do not Reject Ho
p-value: 0.0525
we do not have enough evidence to support the claim that take the random samples of 5 students who have taken the class and 5 students who have not taken the class