Question

7.1 Practice Problems Use the order of operations to calculate the margin of error for each problem. Where requested, identify the variables. Show all of your work. 1. On a recent promotion exam, 34 candidates passed the exam out of a total of 77 candidates. At the 95% confidence level (za/2 = 1.96), calculate the margin of error for the proportion who passed. P = - = 0.442 Y n Q = 1 -.442 = 0.558 n = 77 E = 2a/2 = 0.111 n 196 = 18,028 2. One statistical study of 325 youth showed that 10% of them smoke. What is the margin of error for percentage of smokers, if we want to be 95% confident (za/2 = 1.96)? 10.111-0.1) 0.588 E = 325 1=0.033 3. Calculate the margin of error for a mean, with population standard OR deviation unknown, when the sample standard deviation is 3.59, the sample size is 51 and the t critical value is 2.009. The equation for the margin of error is given below: = 1.010 3.3% E = ta/2 4. Calculate the margin of error for mean per capita income in Appalachian counties. The critical value for a sample of 300 Appalachian counties is ta/ = 1.97 with a sample standard deviation of 4221 dollars. FE

Answer 1

Solution ? Given 325 ô = 0.10 Q = 1-0,10 - 0.90 Za = 1.96 Margin of error = 2012 1.96 0.10 xogo 325 0.032616 Margin of erros foro percentage=G= 0.032616 X100 = 3.2616 % E Given n = 300 tx2= 1.97 s = 4221 Margin of essor = E= taa S 1.97x 4221 V307 E = 477.651