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Do Homework-Corey Johnson- Google Chrome ure Secure I m/Student/playerHomework aspx 5. MTH 140 NN 201702 DTR Homework: Unit 4 Assignment 1 Score: 0 of 1 pt 17 of 20 (14 complete) HW Score: 54.93%, 10.99 of 20 pts 6.3.17-T EQuestion Help A wishes to estimate, with confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 3% of the true proportion. a) No preliminary estimate is available. Find the minimum sample size needed. om b Find the minimum size needed, using a prior study that found that 44% of the respondents said they think their president can control the price of gasoline c) Compare results from parts (a) and (b) (a) What is the minimum sample size needed assuming that no prior information is available? ns (Round up to the nearest whole number as needed) to Enter your answer in the answer box and then click check Answer

Explanation / Answer

we shall use the margin of error formula to solve this proble, where

MOE = Z*sqrt(p*(1-p)/n) , we shall sove this equation for n to arrive at the sample size

Let p is estimate proportion, then we know that z for 90% is 1.64

        Z0.1/2*(p*(1-p)/n)1/2 = 0.03 => 1.64*(p*(1-p)/n)1/2 = 0.03

while for p*(1-p), when p=1/2, p*(1-p) arrive maximum and maximum value is ¼, so n =2988*1/4 =747

So if no estimate were available for the proportion that support current policy, we need 747 sample size.

now if p is given as 44% , then we put p = 0.44 in the same equation and solve for n

Z0.1/2*(p*(1-p)/n)1/2 = 0.03 => 1.64*(0.44*(1-0.44)/n)1/2 = 0.03

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