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18.01.2021 •
Mathematics
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Ответ:
The null and alternative hypotheses:
H0: attitudes between first survey and second survey have not changed.
H1:attitudes between first survey and second survey have changed.
Let's find the observed and expected value using the following:
Observed value = sample size * observed proportion
Expected value = sample size * expected proportion.
Optimistic:
expected= 6%*380=22.8
observed=1%*380=3.8
(fo-fe)²/fe = 15.83333
Slightly Optimistic:
expected: 29%*380=110.2);
Observed: 30%*380= 114
(fo-fe)²/fe = 0.131034
Slightly Pessimistic:
expected= 24%*380= 91.2
Observed = 28%*380=106.4
(fo-fe)²/fe = 2.533333
Pessimistic:
Expected = 41%*380 =155.8
Observed = 41%*380 =155.8
(fo-fe)²/fe = 0
Total (fo-fe)²/fe =
15.83333 + 0.131034 + 2.533333 + 0 = 18.4977
Degrees of freedom, df = 4 - 1 = 3
For chi square test statistic:
Σ(fo-fe)²/fe = 15.83333 + 0.131034 + 2.533333 + 0 = 18.498
Calculate pvalue.
Calculating for pvalue at, df = 3, chi-square score = 18.4977, α=0.05
Pvalue = 0.000347
Decision:
Since pvalue, 0.000347 is less than significance level, 0.05, reject null hypothesis H0.
Conclusion:
There is enough evidence to conclude that there is a change in attitudes between first survey and the second survey at a level of significance, 0.05.