# The accompanying two-way table was constructed using data in the article “Television Viewing and Physical Fitness in Adults” (Research Quarterly for Exercise and Sport, 1990: 315–320).

The accompanying two-way table was constructed using data in the article “Television Viewing and Physical Fitness in Adults” (Research Quarterly for Exercise and Sport, 1990: 315–320). The author hoped to determine whether time spent watching television is associated with cardiovascular fitness. Subjects were asked about their television-viewing habits and were classified as physically fit if they scored in the excellent or very good category on a step test. We include MINITAB output from a chi-squared analysis. The four TV groups corresponded to different amounts of time per day spent watching TV (0, 1–2, 3–4, or 5 or more hours). The 168 individuals represented in the first column were those judged physically fit. Expected counts appear below observed counts, and MINITAB displays the contribution to $$\displaystyle{x}^{{{2}}}$$ from each cell.
State and test the appropriate hypotheses using $$\displaystyle\alpha={0.05}$$
$$\begin{array}{|c|c|}\hline & 1 & 2 & Total \\ \hline 1 & 35 & 147 & 182 \\ \hline & 25.48 & 156.52 & \\ \hline 2 & 101 & 629 & 730 \\ \hline & 102.20 & 627.80 & \\ \hline 3 & 28 & 222 & 250 \\ \hline & 35.00 & 215.00 & \\ \hline 4 & 4 & 34 & 38 \\ \hline & 5.32 & 32.68 & \\ \hline Total & 168 & 1032 & 1200 \\ \hline \end{array}$$
$$Chisq= 3.557\ +\ 0.579\ +\ 0.014\ +\ 0.002\ +\ 1.400\ +\ 0.228\ +\ 0.328\ +\ 0.053=6.161$$
$$\displaystyle{d}{f}={3}$$

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Step 1
Testing for Independence - Lack of Association
When testing null hypothesis

versus alternative hypothesis
is not true.
Let

under regularity conditions, test statistic value is

has approximated a chi-square distribution with (I - 1)(J - 1) degrees of freedom when ${H}_{0}$ is true.
The P-value is corresponding area to the right of curve.
The null hypothesis is
Television viewing and physical fitness are independent
versus alternative
Television viewing and pshysical fitness are not independent.
Critical value, from the table in the appendix, is given by

and the calculated ${X}^{2}$ is given in the output as

thus, since

do not reject null hypothesis at given significance level. The data indicates that there is no association between variables.