More on NAEP test scores. Suppose that you give the NAEP test to an SRS of1000 people

Chapter 0, Problem 14.1

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More on NAEP test scores. Suppose that you give the NAEP test to an SRS of1000 people from a large population in which the scores have mean 280 andstandard deviation = 60. The mean x of the 1000 scores will vary if you takerepeated samples.(a) The sampling distribution of x is approximately Normal. It has mean = 280. What is its standard deviation?(b) Sketch the Normal curve that describes how x varies in many samples fromthis population. Mark the mean = 280. According to the 689599.7 rule,about 95% of all the values of x fall within of the mean. What is themissing number? Call it m for margin of error. Shade the region from the meanminus m to the mean plus m on the axis of your sketch, as in Figure 14.1.(c) Whenever x falls in the region you shaded, the true value of the populationmean, = 280, lies in the confidence interval between x m and x + m. Drawthe confidence interval below your sketch for one value of x inside the shadedregion and one value of x outside the shaded region. (Use Figure 14.3 as a modelfor your drawing.)