Question

The National Unemployment Rate for April 2020 was 14.7%. This is the highest since the Great Depression. Many believe that the county is significantly worse than the nation as a whole. In a recent study of a randomly selected 1,200 adults in the county, 15.5% had filed for unemployment in April. Is this evidence that the proportion of unemployment filers in the county is significantly higher than the National Unemployment Rate? Assume a significance level of 0.05.

Part 1 : Write the conditions for inference.

Answer 1

Part 1)

Condition check for Normal Approximation to Binomial
n * P >= 10 = 1200 * 0.155 = 186
n * (1 - P ) >= 10 = 1200 * ( 1 - 0.155 ) = 1014
Hence both the conditions are satisfied.

To Test :-

H0 :- P = 0.147
H1 :- P > 0.147

Test Statistic :-
Z = ( P - P0 ) / √ ((P0 * q0)/n))
Z = ( 0.155 - 0.147 ) / √(( 0.147 * 0.853) /1200))
Z = 0.7826

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Z(α) = Z(0.05) = 1.645
Z < Z(α) = 0.7826 < 1.645, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence to support the claim that the proportion of unemployment filers in the county is significantly higher than the National Unemployment Rate.