12) A national standardized math test is given to 8th-grade students. Scores on the test range from 0 to 500. Suppose you give this test to an SRS of 900 eighth-graders from a large population in which the scores have a mean μ =285 and a standard deviation σ= 125. The sample mean x-bar will vary if you take repeated samples. Assume the 68-95-99.7 Rule applies. a) If the sampling distribution of x-bar is approximately Normal and has a population mean of 285. What is its standard deviation? b) Suppose that an SRS of 900 eighth-graders has x-bar = 288. Based on this sample, calculate the 95% confidence interval for μ c) Without calculating, suppose we compute a 68% confidence interval for the population mean, would you expect the margin of error to be larger or smaller than that calculated in (b). Why? d) Without calculating, suppose that we take an SRS of 1600 8th-graders and find the sample mean to be 288. Compared to part (b), would the margin of error for a 95% confidence interval for the population mean be larger or smaller. Why?

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.