SOLUTION: 1. The pass rate for Calculus I students at the University of Marin is 45%. Dr Lovemath has a new way of teaching and thinks her methods will improve pass rates. As evidence, she

Question 1115606: 1. The pass rate for Calculus I students at the University of Marin is 45%. Dr Lovemath has a new way of teaching and thinks her methods will improve pass rates. As evidence, she says she taught the class using her new methods and 27 of 52 students passed. Is this enough evidence to conclude her method is better?

1b. The dean of the University of Marin wants to make a report to its board and asks Dr Lovemath to find a 90% confidence interval for the pass-rates for Calculus I with an error of no more than 5%. How many students would she need to test her methods on to create that confidence interval?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The pass rate for Calculus I students at the University of Marin is 45%. Dr Lovemath has a new way of teaching and thinks her methods will improve pass rates. As evidence, she says she taught the class using her new methods and 27 of 52 students passed. Is this enough evidence to conclude her method is better?
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Ho: p = 0.45
Ha: p > 0.45 (claim)
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p-hat = 27/52 = 0.5192
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z(0.5192) = (0.5192-0.45)/sqrt[0.45*0.55/52] = 1.0035
p-value = P(z > 1.0035) = normalcdf(1.0035,100) = 0.1578
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Since the p-value is greater than 10%, fail to reject Ho at the
10% confidence level.
The test results do not support the claim.
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1b. The dean of the University of Marin wants to make a report to its board and asks Dr Lovemath to find a 90% confidence interval for the pass-rates for Calculus I with an error of no more than 5%. How many students would she need to test her methods on to create that confidence interval?
Since Margin of Error = z*sqrt[pq/n], sqrt(n) = [z*sqrt(pq)]/ME
n = [0.1645/0.05]^2*0.45*0.55 = 268 when rounded up
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Cheers,
Stan H.
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