1Suppose a random sample of size 40 is selected from a popul

1.Suppose a random sample of size 40 is selected from a population with = 9. 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 N = 500 (to 2 decimals).

2.The Democrat and Chronicle reported that 25% of the flights arriving at the San Diego airport during the first five months of 2001 were late (Democrat and Chronicle, July 23, 2001). Assume the population proportion is p = .25.

a.What is the probability that the sample proportion will be within +/- .03 of the population proportion if a sample of size 800 is selected (to 4 decimals)?

b.What is the probability that the sample proportion will be within +/- .03 of the population proportion if a sample of size 400 is selected (to 4 decimals)?

Solution

1.

As

SE = s * fpc / sqrt(n)

and

fpc = sqrt[(N-n)/(N-1)]

As N = 500, n = 40,

fpc = sqrt((500-40)/(500-1)) = 0.960126912

Thus,

SE = 9*0.960126912/sqrt(40) = 1.366284548 [ANSWER]

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