Question

Suppose that 20% of American workers aged 60 to 65 years plan to retire in the next 5 years. Suppose we obtain a simple random sample of 1600 workers aged 60 to 65. What is the probability that at least 23% people in the sample plan to retire in the next 5 years?

Answer 1

0.0013

Explanation:

We have p = 20% = 0.20

Sample n = 1600

We are to find probability of at least 23% retiring in 5 years

P(p hat >= 0.23)

We find the z score

Z = p hat - p/√p(1-p/n

= 0.23-0.20/√0.20(1-0.20/1600

= 0.03/0.01= 3

P(z>=3)

1-p(z<3)

1-0.9987

= 0.0013

So we conclude that this is the probability at least 23% people in the sample would retire in the next 5 years