To determine Draw a graph of sentence complexity score for each of the two income groups. Compare the distributions of sentence complexity score for the two income groups. Explanation Calculation: The data represent the summary statistics for the sentence complexity score of low income group and middle income group. Furthermore, it is given that the distribution of sentence complexity score of two income groups are mound shaped and symmetric. If the frequency distribution of the data sets is mound shaped, and symmetric, then the empirical rule can be used as the rule of thumb. Since, the distributions of both the groups are mound shaped and symmetric, the empirical rule can be applied. Empirical rule: For symmetric and mound shaped distributions, 68% of values fall within the interval x ¯ ± 1 s . 95% of values fall within the interval x ¯ ± 2 s . 99.7% of values fall within the interval x ¯ ± 3 s . Empirical rule for the low income group: From the given summary table, the mean, and standard deviation of sentence complexity scores for low income group are 7.62, and 8.91, respectively. That is, x ¯ = 7.62 and s = 8.91 . 1 standard deviation limits: x ¯ ± 1 s = 7.62 ± 1 ( 8.91 ) = [ 7.62 − 1 ( 8.91 ) , 7.62 + 1 ( 8.91 ) ] = [ 7.62 − 8.91 , 7.62 + 8.91 ] = ( − 1.29 , 16.53 ) Thus, 68% of the sentence complexity scores of low income group fall within the interval ( − 1.29 , 16.53 ) . 2 standard deviation limits: x ¯ ± 2 s = 7.62 ± 2 ( 8.91 ) = [ 7.62 − 2 ( 8.91 ) , 7.62 + 2 ( 8.91 ) ] = [ 7.62 − 17.82 , 7.62 + 17.82 ] = ( − 10.2 , 25.44 ) Thus, 95% of the sentence complexity scores of low income group fall within the interval ( − 10.2 , 25.44 ) . 3 standard deviation limits: x ¯ ± 3 s = 7.62 ± 3 ( 8.91 ) = [ 7.62 − 3 ( 8.91 ) , 7.62 + 3 ( 8.91 ) ] = [ 7.62 − 26.73 , 7.62 + 26.73 ] = ( − 19.11 , 34.35 ) Thus, 99.7% of the sentence complexity scores of low income group fall within the interval ( − 19.11 , 34.35 ) . Histogram of the sentence complexity scores of low income group: Step by step procedure to draw the histogram for the sentence complexity scores of low income group is given below. Draw a horizontal axis and a vertical axis. The horizontal axis represents the sentence complexity scores. The vertical axis represents the relative frequencies. Consider the limit points obtained from the empirical rule as the values of horizontal axis (–19.11, –10, –1.29, 7.62, 16.53, 25.44, 34.35). Based on the empirical rule, approximately plot the percentage of each of the intervals on the horizontal axis –19

13th Edition

ISBN: 9780134080215

Author: James T. McClave, Terry T Sincich

Publisher: PEARSON

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Chapter 2, Problem 202ACI

To determine

Draw a graph of sentence complexity score for each of the two income groups.

Compare the distributions of sentence complexity score for the two income groups.

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Chapter 2, Problem 201ACI

Chapter 2, Problem 203ACI

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