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 type I and type II errors in this case, consequences of each error type for this situation, and the appropriate alpha level to use.

Answer 1

Null Hypothesis H0: Alaska had proportion of identity theft equal to 23%

Alternative Hypothesis Ha: Alaska had a lower proportion of identity theft than 23%

Sample proportion, p = 321 / 1432 = 0.224162

Standard error of sample =

Test statistic, z = (0.224162 - 0.23) / 0.01102034 = -0.5297

P-value = P(z < -0.5297) = 0.2982

As, p-value is greater than 0.05, we fail to reject H0 and conclude that there is no significant evidence that Alaska had a lower proportion of identity theft than 23%.

Type I error is that we conclude that Alaska had a lower proportion of identity theft than 23% but in reality Alaska had proportion of identity theft equal to 23%.

Type II error is that we fail to conclude that Alaska had a lower proportion of identity theft than 23% but in reality Alaska had a lower proportion of identity theft than 23%

The appropriate alpha level to use is 0.05.