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# According to the February 2008 Federal Trade Commission

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.

(i) Which of the following statements correctly defines the null hypothesis *H * * _{O } *?

A. *p = * 321

B. * p * < 0.23

C. *p * = 0.23

D. *p < * 321

(ii) Which of the following statements correctly defines the alternate hypothesis *H * * _{A } *?

A. *p = * 321

B. *p * < 0.23

C. *p * = 0.23

D. *p < * 321

(iii) Enter the level of significance used for this test:

*Enter in decimal form. Examples of correctly entered answers: *0.01 0.02 0.05 0.10

(iv) Determinepˆ

*Enter in decimal form to nearest ten-thousandth. Examples of correctly entered answers: *

0.0001 0.0020 0.0500 0.3000 0.7115

(v) Do values for *np * and *nq * both exceed 5? *Enter * YES *or * NO *for answer *

(vi) Calculate and enter test statistic

*Enter value in decimal form rounded to nearest thousandth, with appropriate sign (no spaces). Examples of correctly entered answers: *

–2.014 –0.370 +0.600 +1.009

(vii) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic.

*Enter value in decimal form rounded to nearest thousandth. Examples of correctly entered answers: *

0.000 0.001 0.030 0.600 0.814 1.000

(viii) Comparing p-value, which is the correct decision to make for this hypothesis test?

A. Reject *H * * _{o } *

B. Fail to reject *H * * _{o } *

C. Accept *H * * _{o } *

D. Accept *H * * _{A } *

(ix) Select the statement that most correctly interprets the result of this test:

A. The result is statistically significant at .05 level of significance. Evidence supports the claim that the proportion of complaints due to identity theft in Alaska is less than 23%.

B. The result is statistically significant at .05 level of significance. There is not enough evidence to show that the proportion of complaints due to identity theft in Alaska is not less than 23%.

C. The result is not statistically significant at .05 level of significance. There is not enough evidence to show that the proportion of complaints due to identity theft in Alaska is less than 23%.

D. The result is not statistically significant at .05 level of significance. Evidence supports the claim that the proportion of complaints due to identity theft in Alaska is not less than 23%.

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