Question

In a recent study of a random sample of 113 people, 92 reported dreaming in color. In the 1940’s, the proportion of people who reported dreaming in color was 29%. Is there evidence to show that the proportion of people who dream in color is different than the proportion in the 1940’s? What is the p-value for this hypothesis test?

In a recent study of a random sample of 113 people, 92 reported dreaming in color. In the 1940’s, the proportion of people who reported dreaming in color was 29%. Is there evidence to show that the proportion of people who dream in color is different than the proportion in the 1940’s? What is the test statistic for this hypothesis test?

In a recent study of a random sample of 113 people, 92 reported dreaming in color. In the 1940’s, the proportion of people who reported dreaming in color was 29%. Is there evidence to show that the proportion of people who dream in color is different than the proportion in the 1940’s? What is the critical value for this hypothesis test?

In a recent study of a random sample of 113 people, 92 reported dreaming in color. In the 1940’s, the proportion of people who reported dreaming in color was 29%. Is there evidence to show that the proportion of people who dream in color is different than the proportion in the 1940’s? What is the decision for this hypothesis test?

Answer 1

To Test :-

H0 :- P = 0.29

H1 :- P 0.29

n = 113
P = X / n = 92/113 = 0.8142

Test Statistic :-


Z = 12.28

Test Criteria :-
Reject null hypothesis if
Critical value
= 12.28 > 1.96, hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = 2 * P ( Z > 12.28 )
P value = 0
Reject null hypothesis if P value <
Since P value = 0 < 0.05, hence we reject the null hypothesis
Conclusion :- We Reject H0

There is sufficient evidence to support the claim that the proportion of people who dream in color is different than the proportion in the 1940’s.