Question

Consider a population proportion p = 0.88.

a-1. Calculate the expected value and the standard error of P−P− with n = 30.

a-2. Is it appropriate to use the normal distribution approximation for P−P− ?

b-1. Calculate the expected value and the standard error of P−P− with n = 60.

b-2. Is it appropriate to use the normal distribution approximation for P−P− ?

Answer 1

Given that,

p = 0.88

a)

1 )

1 - p = 1-0.88 = 0.12

n = 30

expected value = = p = 0.88

standard error = =  [p( 1 - p ) / n] = [0.88*(0.12) /30 ] = 0.0593

2) No.

b)

1 )

n = 60

expected value = = p = 0.88

standard error = =  [p( 1 - p ) / n] = [0.88*(0.12) /60 ] = 0.0420

2) Yes.

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