Question

A newspaper poll asked respondents if they trusted "eco friendly" labels on cleaning products. Out of 1000 adults surveyed, 540 responded "yes." We would like to determine if the proportion of respondents that trust these labels is greater than 50%. What is your conclusion using α = 0.05? What is the p-value?

Answer 1

To Test :-

H0 :- P = 0.50

H1 :- P > 0.50

n = 1000
P = X / n = 540/1000 = 0.54

Test Statistic :-


Z = 2.5298   2.53

Test Criteria :-
Reject null hypothesis if

= 2.5298 > 1.6449, hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = P ( Z > 2.5298 )
P value = 0.0057
Reject null hypothesis if P value <
Since P value = 0.0057 < 0.05, hence we reject the null hypothesis
Conclusion :- We Reject H0

There is sufficient evidence to support the claim that the proportion of respondents that trust these labels is greater than 50%