Question

Question 1 options:

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.  μ = 321

B.  p < 0.23

C.  p = 0.23

D.  μ < 321

Enter letter corresponding to correct answer

(ii) Which of the following statements correctly defines the alternative hypothesis H_A?

A.  μ = 321

B.  p < 0.23

C.  p = 0.23

D.  μ < 321

Enter letter corresponding to correct answer

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

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

(iv)  Determine pˆ{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi mathvariant="bold">iv</mi></mfenced><mo mathvariant="bold">&#xA0;</mo><mo mathvariant="bold">&#xA0;</mo><mi mathvariant="bold">Determine</mi><mo mathvariant="bold">&#xA0;</mo><mover><mi mathvariant="bold">p</mi><mo mathvariant="bold">^</mo></mover></math>"}

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 and α 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

Enter letter corresponding to correct answer.

(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%.

Enter letter corresponding to most correct answer

Answer 1

Let p denotes the true proportion of identity theft in Alaska .

i) Null hypothesis : H₀ : p = 0.23

ii) Alternative hypothesis H_A : p < 0.23

iii) level of significance

iv) n*p = 1432*0.23 = 329.36 > 5 and n*q = n*(1 - p)= 1432*(1-0.23) = 1102.64 > 5

v) Yes

vi) The value of test statistic z = -0.52

vii) p-value = 0.3

viii) B. Fail to reject H_o

ix) 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%.