A random sample of 12 university student was drawn in order to determine if a fi
ID: 3224237 • Letter: A
Question
A random sample of 12 university student was drawn in order to determine if a film affected religious tolerance. Pre and post film ratings of religious tolerance were obtained. A higher number represents higher tolerance. The following data were obtained: (a). State the nondirectional alternative hypothesis. (b). State the null hypothesis. (c). Using the sign test, what is the probability of obtaining an outcome at least this extreme (i.e., the outcome or a result even more extreme) if the null hypothesis is true? (d). Using a two-tailed alpha level of .01, what would one conclude?Explanation / Answer
Part a
Solution:
The non-directional alternative hypothesis is given as below:
Alternative hypothesis: Ha: There is a significant difference in the pre and post film ratings.
Ha: µ1 µ2
Part b
Solution:
The null hypothesis is given as below:
Null hypothesis: H0: There is no any significant difference in the pre and post film ratings.
H0: µ1 = µ2
Part c
Solution:
Here, we have to find the probability of obtaining an outcome at least this extreme if the null hypothesis is true. This means we have to find the P-value for the sign test.
The test is summarised as below:
Post film
Pre film
d
80
50
30
72
70
2
60
50
10
85
80
5
64
60
4
37
30
7
42
32
10
55
50
5
67
70
-3
87
80
7
82
85
-3
80
77
3
Ranks
N
Mean Rank
Sum of Ranks
Pre_film - Post_film
Negative Ranks
10a
7.20
72.00
Positive Ranks
2b
3.00
6.00
Ties
0c
Total
12
a. Pre_film < Post_film
b. Pre_film > Post_film
c. Pre_film = Post_film
Test Statisticsb
Pre_film - Post_film
Z
-2.596a
Asymp. Sig. (2-tailed)
.009
a. Based on positive ranks.
b. Wilcoxon Signed Ranks Test
Required probability = 0.09
(Calculated by using excel or other technology.)
Part d
Solution:
For two tailed test,
We get p-value = 0.009 < Alpha = 0.01, so we reject the null hypothesis that there is no any significant difference in the pre and post film ratings.
This means we conclude that there is sufficient evidence that there is a significant difference in the pre and post film ratings.
Post film
Pre film
d
80
50
30
72
70
2
60
50
10
85
80
5
64
60
4
37
30
7
42
32
10
55
50
5
67
70
-3
87
80
7
82
85
-3
80
77
3
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