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%?

Test at the 5% level.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.23

H_a : p < 0.23

= x / n = 321 / 1432 = 0.2242

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.2242 - 0.23/ [(0.23 * 0.77) / 1432]

= -0.525

P-value = 0.2998

= 0.05

P-value >

Fail to reject the null hypothesis .

There is not enough evidence to suggest that   Alaska had a lower proportion of identity

theft than 23% .