Question

A study was conducted to see if people who use the Internet have also paid to download music. In a representative sample of 771 adults who use the Internet, 507 admitted that they have paid to download music. Let p represent the true proportion of all Internet-using adults who have paid download music. Complete parts a through g below. a. Compute a point estimate of p. The point estimate of p is (Round two decimal places as needed.) to download music exceeds 0.7 Set up the null and alternative hypotheses for testing whether the true proportion all Internet-using adults v have pa What are the hypotheses for this test? O B. Ho: D=0.7 O A. Ho: p0.7 H p 0.7 Hp0.7 O D. H p 0.7 H p0.7 O C. Ho: p 0.7 Hp#0.7 O F. Hn p 0.7 H ps0.7 O E Ho: p #0.7 Hp 0.7 .Compute the test statistic for part b. z (Round to two decimal places as needed.) Find the rejection region for the test if a= 0.10. Select the correct choice below and fill in the answer box(es) o complete your choice. (Round to three decimal places as needed.) O A. z| O B. z O C. z or z O D. z< e. Find the p-value for the test. p-value (Round to three decimal places as needed.) f. Make the appropriate conclusion using the rejection region. in the reiection reaion. Therefore, there is evidence at the 0.10 level of significance to indicate that the true proportion of all the null hypothesis because the test statistic Internet-using adults who have paid to download music exceeds 0.7. g. Make the appropriate conclusion using the p-value. the null hypothesis because the p-value is a0.10. Therefore, there is t the 0.10 Jevel of sianificance to indicate that the true proportion of all Internet-using evidence adults who have paid to download music exceeds 0.7

Answer 1

Sample size (n) = 771

Users of internet (x) = 507

= x/n = 507/771 = 0.658

P

1. The point estimate of p is 0.66

2. The hypotheses of this test are

H₀: p = 0.7

H_a: p > 0.7

3. Test statistics: Z = (
   P
   – P₀) / √ (P₀ (1 - P₀) / n)

                           Z = (0.66 - 0.7) / √ ((0.7)*(1-0.7)/771)

                           Z = -2.424

4. One sided z critical values at α = 0.10 is Z_α = Z₀ = 1.282

Rejection region: Reject H₀ if Z > 1.282.

5. This is one sided test so we find the right tailed probability.

P value = P(Z > -2.424 ) = (1 - NORM.S.DIST(-2.424,TRUE)).. (Using excel function)

P value = 0.992

6. Failed to reject the null hypothesis because test statistics not lies in rejection region. Therefore, there is not enough evidence at 0.10 level of significance to indicate that the claim that the true proportion of all Internet-using adults who have paid to download music exceeds 0.7.

7. Failed to reject the null hypothesis because p-value is not less than α = 0.10. Therefore, there is not enough evidence at 0.10 level of significance to indicate that the claim that the true proportion of all Internet-using adults who have paid to download music exceeds 0.7.