Question

We will track an SRS of 300 recent PCC Math 243 students to see if they eventually take Math 244. Assume 15% of all PCC Math 243 students eventually take Math 244. The exact probability that p-hat will be not less than 18% is between: ???

Please show all steps and how to use calculate

Answer 1

SOLUTION:

From given data,

We will track an SRS of 300 recent PCC Math 243 students to see if they eventually take Math 244. Assume 15% of all PCC Math 243 students eventually take Math 244. The exact probability that p-hat will be not less than 18% is between

Find the probability that the proportion of success will be not less than 18%.

p = 18% = 18/100 = 0.18

E(p) = 15% = 15/100 = 0.15

n = 243

SE(p) = sqrt (E(p)(1-E(p)) / n)

SE(p) = sqrt (0.15 (1-0.15) / 243)

SE(p) = 0.0229

Consider,

P(P > 0.18) = P ( p-E(p) / SE(p) > 0.18 - E(p) / SE(p) )

P(P > 0.18) = P ( z  > 0.18 - 0.15 / 0.0229)

P(P > 0.18) = P ( z  > 0.03 / 0.0229)

P(P > 0.18) = P ( z  > 1.31)

P(P > 0.18) = 1 - P ( z  < 1.31)

P(P > 0.18) = 1 - 0.9049 (from standard normal table)

P(P > 0.18) = 0.0951

P(P > 0.18) = 9.5%

standard normal table