Question

It is reported that nationwide, 14.6% of the population lives in poverty conditions. A survey of n = 850 individuals in a country, whose population is more than 20,000, included 109 living in poverty conditions. Is this significant evidence that the proportion of individuals living in poverty conditions in this country is less than the national proportion? Use alpha = 0.05.

1. state hypothesis

2. draw rejection region

3. calculate test statistic

4. find p-value

5. state conclusion in terms of problem

6. state/check any assumptions made

Answer 1

To Test :-

H0 :- P = 0.146

H1 :- P < 0.146

n = 850
P = X / n = 109/850 = 0.1282

Test Statistic :-


Z = -1.4697

Test Criteria :-
Reject null hypothesis if

= -1.4697 > -1.645, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( Z < -1.4697 )
P value = 0.0708
Reject null hypothesis if P value <
Since P value = 0.0708 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Assumption

np > 5 i.e 850 * 0.146 = 124.1 > 5

nq > 5 i.e 850 * ( 1 - 0.146 ) = 25.9 > 5

Hence the condition is satisfied.