A sample of size 100 is selected from a population with p = .40. a. What is the

Question

A sample of size 100 is selected from a population with p = .40. a. What is the expected value of p? b. What is the standard error of p? c. Show the sampling distribution of p. d. What does the sampling distribution of p show? A population proportion is .40. A sample of size 200 will be taken and the sample population will be used to estimate the population proportion. a. What is the probability that the sample proportion will be within plusminus.03 of the population proportion? b. What is the probability that the sample proportion will be within plusminus .05 of the population proportion? Assume that the population proportion is .55. Compute the standard error of the F population, sigma_p, for sample sizes of 100, 200, 500, and 1000. What can you say about the the standard error of the proportion as the sample size is increased?

Explanation / Answer

Sol31a:

Expected value=0.40

Solution31b:

standard error=sqrt[(0.4)(1-0.4)/100]=0.0489

Solution33:

SE=for n=100 is

p=0.55 given

SE1=sqrt[0.55(1-.0.55)/100]=0.049

SE2 for n=200

SE2=sqrt[0.55(1-0.55)/200]=0.035

SE3 =for n=500

SE3=SQRT[0.55(1-0.55)/500]=0.022

SE4 for n=1000

SE4=sqrt[0.55(1-0.55)/1000]=0.016

as sample size increased form 100 to 1000 the standard error decreased from 0.049 to 0.016

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