6. (20 points) How influential can a movie be? A curious researcher asked a rand

Question

6. (20 points) How influential can a movie be? A curious researcher asked a random group of people to rate the Bush administration on a scale from 1 to 10 (with 1 being the least supportive and 10 being the most supportive). She then had them view the anti-Bush movie Fahrenheit 9/11 by Michael Moore after it had just been released and asked them the same question again. Given the results below, choose an appropriate statistic technique to test whether there is difference in the before and after support for the Bush administration. After Fahrenhelt 9/11 Fahrenhelt 9/11 10 2 3 Before Fahrenheit 9/11 Mean=5.92 5-2.94 ~ After Fahrenheit 9/11 I Mean-3.75 S-2.60

Explanation / Answer

Given that,
mean(x)=5.92
standard deviation , s.d1=2.94
number(n1)=12
y(mean)=3.75
standard deviation, s.d2 =2.6
number(n2)=12
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.201
since our test is two-tailed
reject Ho, if to < -2.201 OR if to > 2.201
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =5.92-3.75/sqrt((8.6436/12)+(6.76/12))
to =1.915
| to | =1.915
critical value
the value of |t | with min (n1-1, n2-1) i.e 11 d.f is 2.201
we got |to| = 1.91531 & | t | = 2.201
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.9153 ) = 0.082
hence value of p0.05 < 0.082,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 1.915
critical value: -2.201 , 2.201
decision: do not reject Ho
p-value: 0.082

There is no difference in the before and after support for the bush administration

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