Chapter 11, Problem R11.3RE

a)

To determine

To explain which chi-square test appropriate to given data.

Answer to Problem R11.3RE

Chi-square test of Homogeneity.

Explanation of Solution

When there two variables in the multiple samples then we used chi-square test of Homogeneity to check the distribution of two variables. Therefore, here the variables are Number of televisions in household and year. The samples are collected for 2009 and 2015. Hence, Chi-square test of Homogeneity is appropriate to use.

b)

To determine

To show how the number 252 and 14.113 were obtained for the 2009/None cell.

Explanation of Solution

Given:

Observed count is 192

Row total = r = 366

Column total = c = 14557

Grand total = n = 21177

Formula:

  $E=\frac{r\times c}{n}$

First need to find expected count.

  $E=\frac{366\times 14557}{21177}=252$

Therefore, the chi-square test statistic is,

  ${\chi }^2={\displaystyle \sum \left(\frac{{(192-252)}^2}{252}\right)}=14.113$

c)

To determine

To explain which 3 cells contribute most to the chi-square test statistic.

Explanation of Solution

The contribution of a cell to the chi-square test statistic is the third value mentioned in the cell. Therefore, the highest contributions are 31.034, 27.628 and 23.258, which belong to the cells None/2015, 5 or more/2015 and 1/2015.

Moreover, so the expected count exceeds the observed count in the cells None/2015 and 1/2015, while the observed count exceeds the observed count in the cell 5 or more/2015.