Question

A television sports commentator wants to estimate the proportion of citizens who follow professional football." Complete parts () through (c). Click here to view the standard normal distribution table (page 1) Click here to view the standard normal distribution table (page 2 (a) What sample size should be obtained if he wants to be within 3 percentage points with 98% confidence if he uses an estimate of 54% obtained from a poll? The sample size is (Round up to the nearest integer.) (b) What sample size should be obtained if he wants to be within 3 percentage points with 90% confidence if he does not use any prior estimates? The sample size is (Round up to the nearest integer.) (c) Why are the results from parts (a) and (b) so close? O A The results are close because the confidence 90% is close to 100%, O B. The results are close because 0.541 -0.54)= 0.2484 is very close to 0.25. O C. The results are close because the margin of error 3% is less than 5%

Answer 1

E - Solution Given that 3 % -0.03.... margin of error pl -54% = 0.54. 2 At 96% confidence intervcel zis. c = 96% 0.96. dal-c-1-0.96 = 0.04 3 = 0.04 a 0.02. 3 = 3 = 2.054 using 2 kable] sample size n = ( ² ) P (1-P) - - 2054 205461-0-59) - 1164.42 ł 1165 1165 Answers The sample size is

Solution Given that B 3% = 0.03..... Margin op emos Wher pr is not given then we use of At 96% confidence interval zis بمهمتو يودع RI - C I -0.96 0.04 3.02 = 2.054 using zrable. Sample size n = ( ² Jp(1-P) =42.004) os choose = 1171.92 e 1172 sample sizena 1172 | Answer :- The c. option B. The result are close because 0.54 (1-0.54) 20.2484 is very close to 0.25.