Question

Suppose a random sample of size 12, of which 6 have a certain criteria, is drawn from a population.

a) If we were to use confidence interval procedures based on the normal distribution, what is the zα2  value for a 50 % confidence interval for p, the population proportion?

Round your response to at least 2 decimal places.

b) What is the margin of error for a 50 % confidence interval for p?

Round your response to at least 3 decimal places.

c) Was it reasonable to use the confidence interval procedures in this situation?     Yes or No

Answer 1

Solution,

Given that,

n = 12

x = 6

a)

At 50% confidence level the z is ,

= 1 - 50% = 1 - 0.50 = 0.5

/ 2 = 0.5 / 2 = 0.25

Z_/2 = Z _0.25 = 0.67

b)

Point estimate = sample proportion = = x / n = 6/12 = 0.5

1 - = 1 - 0.5 = 0.5

Z_/2 =  Z 0.25 = 0.67

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 0.67 * (((0.5 * 0.5) /12 )

E = 0.144

c)

Yes