(Solution) - In Formula 6 1 we assume that the population is infinite -(2025 Original AI-Free Solution)

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In Formula 6-1 we assume that the population is infinite, that we are sampling with replacement, or that the population is very large. If we have a relatively small population such that n > 0.05N, and sample without replacement, we should modify £ to include a finite population correction factor as follows:

where N is the population size.
a. Find the 95% confidence interval for the mean of 100 IQ scores if a sample of 31 of those scores produces a mean and standard deviation of 132 and 10, respectively.
b. If you are determining a sample size, and realize that the population size N is relatively small, then the sample-size calculation should be revised to:
For a challenge, try solving the expression given at the beginning of this question for n to produce the formula given here. Repeat Exercise 13, assuming that the statistics students are randomly selected without replacement from a population of N = 200 statistics students.