Suppose an educational television station has broadcast a service of program on
ID: 3153845 • Letter: S
Question
Suppose an educational television station has broadcast a service of program on the physiological and psychological and psychological effects of smoking marijuana now that the series is finished the station wants to see whether the citizens within the viewing area have changed their minds about how possession of marijuana should be considered legally Before the series was shown, it was determined that 7% of the citizens favored legalization, 18% favored decriminalization, 65% favored the existing law (an offender could be fined or imprisoned), and 10% had no opinion. A summary of the opinions (after the series was shown) of a random sample of 500 people in the viewing area is given below text at a alpha = 0.01 level to use whether these data indicate that the distribution of opinions differs significantly from the proportions that existed before the educational series was aired.Explanation / Answer
Solution:
For this test, the null and alternative hypothesis are given as below:
Null hypothesis: H0: The distribution of opinions does not differ than proportions that existed before the educational series was aired.
Alternative hypothesis: Ha: The distribution of opinions is significantly differing than proportions that existed before the educational series was aired.
The test statistic value is given as below:
Chi square = [(O – E)^2 / E ]
The calculations for test statistic value are given as below:
Opinions
Observed
Probability
Expected
(O - E)^2
(O - E)^2 / E
Legalization
39
0.07
35
16
0.457142857
Decriminalization
99
0.18
90
81
0.9
Existing laws
336
0.65
325
121
0.372307692
No opinion
26
0.1
50
576
11.52
Total
500
1
500
13.24945055
d.f. = n - 1 = 4 - 1 = 3
Level of significance = alpha = 0.01
Critical value =
11.3448667
Test statistic value = chi square = 13.25
Here, test statistic value chi square = 13.25 is greater than the critical value 11.34, so we reject the null hypothesis that the distribution of opinions do not differ than proportions that existed before the educational series was aired. This means, we conclude that the distribution of opinions is significantly differing than proportions that existed before the educational series was aired.
Opinions
Observed
Probability
Expected
(O - E)^2
(O - E)^2 / E
Legalization
39
0.07
35
16
0.457142857
Decriminalization
99
0.18
90
81
0.9
Existing laws
336
0.65
325
121
0.372307692
No opinion
26
0.1
50
576
11.52
Total
500
1
500
13.24945055