Question

A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let P denote the proportion in the sample who say they support the increase. Suppose that 25% of all adults in Ohio support the increase. The standard deviation of the sampling distribution is_____ . Round your answer to four decimal places.

Suppose that 83% of all dialysis patients will survive for at least 5 years. In a simple random sample of 100 new dialysis patients, what is the probability that the proportion surviving for at least five years will exceed 80%, rounded to 5 decimal places? _____

Answer 1

a) n = 1500

p = 0.25

Standard deviation = sqrt(p(1 - p)/n)

                                = sqrt(0.25 * (1 - 0.25)/1500)

                                 = 0.0112

b) n = 100

p = 0.83

= p = 0.83

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

       = sqrt(0.83 * (1 - 0.83)/100)

         = 0.0376

P( > 0.8)

= P(( - )/ > (0.8 - )/)

= P(Z > (0.8 - 0.83)/0.0376)

= P(Z > -0.80)

= 1 - P(Z < -0.80)

= 1 - 0.2119

= 0.7881