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

The null and alternative hypothesis

H0: p = 0.23

Ha: p < 0.23

Population parameter is population proportion p.

Random variable = Sample parameter

Sample proportion $\hat{p}$ = 321 / 1432 = 0.2242

Test statistics

z = $\hat{p}$ - p / sqrt [ p (1 - p) / n ]

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

= -0.52

p-value = P(Z < z)

= P(Z < -0.52)

= 0.3015

At 0.05 level, since p > 0.05 , Do not reject H0