Suppose a simple random sample of size 40 is selected from a population with = 1

Question

Suppose a simple random sample of size 40 is selected from a population with = 12. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).

a. The population size is infinite (to 2 decimals).

b. The population size is N = 50,000 (to 2 decimals).

c. The population size is N = 5000 (to 2 decimals).

d. The population size is N = 500 (to 2 decimals).

Explanation / Answer

95% confidence interval (two tails) => value for alpha from P(Z) = 0.975 => 1.96 (X - 1.96(sigma / root(n))) < µ < (X + 1.96(sigma / root(n))) (150.6 - 1.96(24.4 / root(32))) < µ < (150.6 + 1.96(24.4 / root(32))) 142.145... < µ < 159.05... answer A

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