Question

mathxl.com Homework A Programmer Plans To Develop... Do Homework - Morgyn Sallie Homework Margin of Error Calculator - eMat... Standard Deviation Calculator . STAT2303.005 (Spring 2020) J Fatema 10:45 AM Morgyn Sallie & 02/11/20 7:43 PM Homework: Practice Problems 3 - Give Me Some Props Save Score: 0.33 of 1 pt 9 of 30 (29 complete) HW Score: 68.08%, 20.42 of 30 pts 27.1.36-T 13 Question Help O A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 90% confident that his estimate is in error by no more than four percentage points? Complete parts (a) through (c) below. a) Assume that nothing is known about the percentage of computers with new operating systems. n = 423 (Round up to the nearest Integer.) b) Assume that a recent survey suggests that about 96% of computers use a new operating system. n=1 (Round up to the nearest integer.) X 1 ravin (1 More Enter your answer in the answer box and then click Check Answer. 1 pantaining 1 part remaining Clear All Check Answer

Answer 1

Solution: Part-A: For 90% confidence, a = 1 -0.90 = 0.10 From normal distribution table, Za/2 = 20.10/2 = 20.05 = 1.645 Desired maximum margin of error = 4% = 0.04 Margin of error: p1 - p) MoE = 20.05 X V n If we keep the margin of error to be maximum at 4%, then the term p(1 – p) will need to be maximum, which in turn will be maximum at p = 0.5 0.5 x (1 – 0.5) = 0.04 = 1.645 x п →n = 422.8 423(Rounding up) Hence, sample size required = 423 Part-B: Given, p = 96% = 0.96 Margin of error: |p1 – p) MoE = 20.05 In 0.96 x (1 – 0.96) = 0.04 = 1.645 x n =n= 64. 965 (Rounding up) Hence, sample size required = 65