21 We randomly select 1000 adults from a population of 2 mil

21. We randomly select 1000 adults from a population of 2 million and also randomly select 1000 adults from a population of 20 million. If the sample standard deviations are the same, how will the margins of error compare for 95% confidence Intervals for the true population average? Will the margin of error for the sample from the larger population be greater than, the same, or less than the margin of error for the sample from the smaller population> Why> (Provide the reasoning behind your answer) 22. We have calculated a 95% Confidence Interval of the Difference between two Population Proportions. The interval is 4% +/- 5%. Can we conclude that there is a difference between the two group Population Proportions? Yes or No? Why? (Provide the reasoning behind your answer) 23. A group of college age males and a group of college age females were sampled and 95% confidence intervals were created for the true population average of the amount spent on pizza and related items in the past month. The male confidence interval is from $40 to $60 ($50 +/- $10). The female confidence interval is from $25 to $35 ($30 +/- $5). Is there a difference between the two group population mean amounts spent ? Why? (Provide the reasoning behind your answer)(see page 10.4 in the online notes: Statistical Significance and Confidence Intervals)

Solution

21.

The margin of error will be greater for the larger population. This is because the the finite population correction (fpc) is given by

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

where N = population size
n = sample size.

As we can see, as N increases, fpc increases. Hence, the standard error increases with increasing population size.

Thus, the margin of error increases with increasing population size. [ANSWER]

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