Name: 3. A major oil company would like to improve its tarnished image following
ID: 3336152 • Letter: N
Question
Name: 3. A major oil company would like to improve its tarnished image following a large oil spill. It s marketing department develops a short television commercial and on a sample of n = 7 participants. People's attitudes about the company tests it are measured with a short questionnaire, both before and after viewing the commercial. Was there a significant change? The data are as follows: Person After 15 13 18 12 16 10 19 Before Difference 15 10 14 10 a) What type of study design is this? b) What is your null and alternative hypothesis? Record both the statement and the statistical hypotheses using appropriate notation.Explanation / Answer
Solution:
Part a
This is a paired t test.
Part b
The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: There is no any statistically significant change in the people’s attitudes about the company before and after viewing the commercial.
Alternative Hypothesis: Ha: There is a statistically significant change in the people’s attitudes about the company before and after viewing the commercial.
H0: µ1 = µ2 Vs H0: µ1 µ2
The level of significance is given as 0.05.
= 0.05
The test statistic formula is given as below:
t = Dbar / [Sd/sqrt(n)]
Calculation table is given as below:
Before
After
Di
(Di - DBar)^2
15
15
0
56.25
11
13
-2
30.25
10
18
-8
0.25
11
12
-1
42.25
14
16
-2
30.25
1
10
-9
2.25
11
19
-8
0.25
Total
-30
161.75
Sample size = n = 7
Degrees of freedom = n – 1 = 7 – 1 = 6
Dbar = -30/7 = -7.5
Sd = 7.3428
Standard error = Sd / sqrt(n) = 7.3428 / sqrt(7) = 2.775317532
t = Dbar / [Sd/sqrt(n)]
t = -7.5 / [7.3428/sqrt(7)]
t = -2.7024
Lower critical value = -2.4469
Upper critical value = 2.4469
P-value = 0.0355
(By using t table)
P-value < = 0.05
So, reject the null hypothesis that there is no any statistically significant change in the people’s attitudes about the company before and after viewing the commercial.
Part c
Conclusion:
There is sufficient evidence to conclude that there is a statistically significant change in the people’s attitudes about the company before and after viewing the commercial.
Before
After
Di
(Di - DBar)^2
15
15
0
56.25
11
13
-2
30.25
10
18
-8
0.25
11
12
-1
42.25
14
16
-2
30.25
1
10
-9
2.25
11
19
-8
0.25
Total
-30
161.75
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