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m 1-Google Dr x ps://unco.instructure.com/courses/27166/quizzes/140373/take to Ramirez make Children lstro Equity for Learning E Ashlea Campbell Wi(0 Region3-Tesas Disis Univers Sample iestwnswex -University of North ×/-Quit Exami Box Plot p strong D Question 5 20 pts 5. (20 Points) The national average for the percentage of high school graduates taking SAT is 4996, bu t the state averages vary from a low of 4% to a high of 92%. A random particular tristate area, and it was sample of 300 graduating seniors was polled across a found that 195 had taken the SAT (a) Find and interpret a 95% confidence interval for the state population proportion. (b) How many sample size do we need such that with probability 0.95 the error of estimating the state proportion would not exceed 0.1? HTML Editor a. p-hat 0.65 two tailed 1.96 indows HEWLETT-PACKARDExplanation / Answer
p-hat = 195/300 = 0.65
margin of error, E = sqrt(p-hat*q-hat/n)*z_c
= sqrt(0.65*(1-0.65)/300)*1.96
= 0.05397
95% CI = (p-hat - E , p-hat + E )
= ( 0.65 - 0.05397, 0.65 + 0.05397)
= (0.59603, 0.70397
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