=====Mathematics 241 - Spring 2015=====

==== Homework ====

===Homework===

**Section 10.5**

Exercise Set E: 1, 2, 3

Also:

  - The file [[http://dananne.org/fu/courses/math-241/R/pearson.txt|http://dananne.org/fu/courses/math-241/R/pearson.txt]] contains the data from Karl Pearson's study of the heights of 1078 fathers and sons discussed in Section 8.1. The data is in a table, with the first column labeled "Father" and the second column labeled "Son". Recall: If you use RStudio to directly import this file, change the "Separator" selection from "Tab" to "Whitespace".
    - Use this data to create a scatter diagram with regression line, treating the heights of the sons as the dependent variable.
    - Find a 95% prediction interval for the predicted height of a son whose father is 65 inches tall.
    - Find a 95% confidence interval for the average height of sons whose fathers are 65 inches tall.
    - Test the hypotheses $H_0 : \beta = 0$ against the hypothesis $H_1 : \beta \ne 0$, where $\beta$ is the true slope of the regression line.
    - Now use this data to create a scatter diagram with regression line, treating the heights of the fathers as the dependent variable.
    - Find a 95% prediction interval for the predicted height of a father whose son is 65 inches tall.
    - Find a 95% confidence interval for the average height of fathers whose sons are 65 inches tall.
  - The file [[http://dananne.org/fu/courses/math-241/R/reading.txt|http://dananne.org/fu/courses/math-241/R/reading.txt]] contains data from a reading test administered to 40 elementary school students. The test was first given to the students in 1982 and then given a year later to the same students. The data is in a table, with the first column labeled "Y1982" and the second column labeled "Y1983".
    - Use this data to create a scatter diagram with regression line, treating the 1982 data as the //x// variable and the 1983 data as the //y// variable.
    - Find a 95% prediction interval for the predicted score of a student whose 1982 score was 280.
    - Find a 95% confidence interval for the average score of students whose 1982 score was 280.
    - Test the hypotheses $H_0 : \beta = 0$ against the hypothesis $H_1 : \beta \ne 0$, where $\beta$ is the true slope of the regression line.
    - Use this data to create a scatter diagram with regression line, treating the 1983 data as the //x// variable and the 1982 data as the //y// variable.


Answers:

  - 
    - {{:math-241:m241-s15-hw:pearson-scatter-plot.png?direct&300|}}
    - $(62.5, 72.1)$
    - $(67.1, 67.5)$
    - $t = 19.01$, so the //p//-value is less than $2 \times 10^{-16}$
    - {{:math-241:m241-s15-hw:pearson-scatter-plot-2.png?direct&300|}}
    - $(61.2, 70.6)$
    - $(65.7, 66.1)$
  - THe
    - {{:math-241:m241-s15-hw:reading-scatter-plot.png?direct&300|}}
    - $(236.8, 326.7)$
    - $(274.5, 289.0)$
    - $t = 8.774$, so the //p//-value is $1.14 \times 10^{-10}$
    - {{:math-241:m241-s15-hw:reading-scatter-plot-2.png?direct&300|}}