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Statistics: Sampling and Sampling Distributions

1.) Suppose a simple random sample of size 50 from a population with a mean of 10. 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
b.) the population size is N=50,000
c.) the population size is N=5000
d.) the population size is N=500

2.) Time/CNN voter polls monitored public opinion for the presidential candidates during the 2000 presidential election campaign. One poll used a sample of 589 likely voters. Assume the population proportion for a presidential candidate is p=.50. Let p be the sample proportion of likely voters favoring the presidential candidate.

a.) show the sampling destruction of p.
b.) what is the prob. the poll will provide a sample proportion within +/- .04 of the population proportion?
c.) what is the prob. the poll will provide a sample proportion within +/- .03 of the population proportion?
d.) what is the prob. the poll will provide a sample proportion within +/- .02 of the population proportion?

3.) The Rochester Democrat and Chronicle reported that 25% of the flights arriving at the Sand Diego airport during the 1st 5 months of 2001 were late. Assume the population proportion is p=.25

a.) Show the sampling distribution of p, the proportion of late flights in a sample of 1000 flights
b.) What is the probability that the sample proportion will be within +/- .03 of the population proportion if a male of size 1000 is selected
c.) answer part (b) of 500 flights.

Solution Preview

** Please see the attached file for the complete solution response **

1.) Suppose a simple random sample of size 50 from a population with = 10. 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
b.)The population size is N=50,000
c.)The population size is N=5000
d.)The population size is N=500

Solution: (please see the attached file)

(a)

Since population size is finite.

Standard error of mean = (please see the attached file)

(b)

n/N = 50/50000 = 0.001

Since it is less ...

Solution Summary

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