Question

According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints ("Consumer fraud and," 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? State the random variable, population parameter, and hypotheses.

Answer 1

To Test :-

H0 :- P = 0.23

H1 :- P < 0.23

n = 1432
P = X / n = 321/1432 = 0.2242

Test Statistic :-


Z = -0.5215

Test Criteria :-
Reject null hypothesis if

= -0.5215 > -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 < -0.5215 )
P value = 0.301
Reject null hypothesis if P value <
Since P value = 0.301 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence to support the claim that the that Alaska had a lower proportion of identity theft than 23%.