For a given sample proportion p, show that a value o for which the test statistic...

 

Transcribed Image Text:

For a given sample proportion p, show that a value o for which the test statistic z = (p-ло)/√(1-0)/n] takes some fixed value zo (such as 1.96) is a solution to the equation (1+z/n) + (-2p-2/n)лo+p² = 0. Hence, using the formula x = [-b± √(b²-4ac)]/2a for solving the quadratic equa- tion ax² + bx+c = 0, obtain the limits for the 95% confidence interval in Section 1.3.4 for the probability of success when a clinical trial has nine successes in 10 trials. For a given sample proportion p, show that a value o for which the test statistic z = (p-ло)/√(1-0)/n] takes some fixed value zo (such as 1.96) is a solution to the equation (1+z/n) + (-2p-2/n)лo+p² = 0. Hence, using the formula x = [-b± √(b²-4ac)]/2a for solving the quadratic equa- tion ax² + bx+c = 0, obtain the limits for the 95% confidence interval in Section 1.3.4 for the probability of success when a clinical trial has nine successes in 10 trials.

Answer rating: 100% (QA)

n Zo But P 2 Zo n 2 2 2 1 3 22 P 0 ... View the full answer