Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a marketing survey, a random sample of 722 women shoppers revealed that 638 remained loyal to their favorite supermarket during the past year (i.e., did not switch stores). (a) Let p represent the proportion of all women shoppers who remain loyal to their favorite supermarket. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 95% confidence interval for p. (Round your answers to three decimal places.) lower limit upper limit Give a brief explanation of the meaning of the interval. O 5% of all confidence intervals would include the true proportion of loyal women shoppers. 5% of the confidence intervals created using this method would include the true proportion of loyal women shoppers. 95% of the confidence intervals created using this method would include the true proportion of loyal women shoppers. 95% of all confidence intervals would include the true proportion of loyal women shoppers. (c) As a news writer, how would you report the survey results regarding the percentage of women supermarket shoppers who remained loyal to their favorite supermarket during the past year? O Report the confidence interval. Report p. Report the margin of error. Report p along with the margin of error. What is the margin of error based on a 95% confidence interval? (Round your answer to three decimal places.)

Answer 1

Date Page solution! Given that, n=722 X=638 so, P= * = 638 = 0.8837 +22 point estimate '1-p= 0.8837 =0.8837 = 0.1163 At as % confidence level the zis x=1-95 for X=1-0.95 = 0.05 q = 0.05 = 0.025 Z112- 20.025 = 1.96 Margin of error=€ = 26/2 x x (1-0) E=1.96x0.8837x0.1163 722 pis E = 0.023 At as % confidence intervall For р- <p s p +E 0.8837- 0.023 <p < 0.8837 +0.023 0.8607 cpe 0.9067 (0.861, 0.907)

b) The 95 % confidence interval for p is Lower limit = 0.861 1 upper limit = 0.907 as o% confidence intervals Created using this method would include the true proportion of loyal women'' shoppers. of the confidence interval. con The margin of error based ona as % confidence - intervalo 0.023