Sample size and margin of error. High school students who take the SATmathematics exam a

Chapter 0, Problem 14.7

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Sample size and margin of error. High school students who take the SATmathematics exam a second time generally score higher than on their first try.The change in score has a Normal distribution with standard deviation = 50.A random sample of 1000 students gains an average of x = 22 points on theirsecond try.5(a) Give a 95% confidence interval for the mean score gain in the populationof all students.(b) Suppose that the same result, x = 22, had come from a sample of250 students. Give the 95% confidence interval for the population mean inthis case.(c) Suppose that a sample of 4000 students had produced the sample meanx = 22. Again give the 95% confidence interval for .(d) What are the margins of error for samples of size 250, 1000, and 4000? Howdoes increasing the sample size change the margin of error of a confidenceinterval?