According to ORC International 71 of Internet users connect

According to ORC International, 71% of Internet users connect their computers to the Internet by normal telephone lines. Assume a population proportion = 0.71.

a. What is the expected value of the statistic? ____________ (to 2 decimals)

b. What is the standard error of the statistic? ____________ Assume the sample size is 350. (to 3 decimals)

c. What is the probability that a sample proportion from a simple random sample of 350 Internet users will be within ±0.05 of the population proportion? _________________

d. What is the probability that a sample proportion from a simple random sample of 350 Internet users will be 0.75 or greater?

Solution

a)

expected value = 0.71

b)

Se = srqt [( 0.71 * 0.29) / 350 ]

Se = 0.02425

c)

P ( -0.05 / 0.02425 < z < 0.05 / 0.02425 )

P( -2.06 < z < 2.06 ) = 1 - 0.0197 - 0.0197 = 0.9606

d)

P( z > 0.75 )

P( z > [ 0.75 - 0.71 ] / 0.02425 )

P( z > 1.65 ) = 0.0495