Chapter 10.1, Problem 10.20E

(a)

To determine

To Calculate: the chi-square statistics and p-value.

Answer to Problem 10.20E

  $H_0:$ There is no connection between smoking and Drinking.

  $H_1:$ There is a connection between smoking and Drinking.

Explanation of Solution

Given:

Alcohol consumption	Smoked	Did not smoke
Yes	20	13
No	48	96

Formula used:

  ${\chi }^2={\displaystyle \sum \frac{{\left(O-E\right)}^2}{E}}$

  $E=np$

Assume

  $\alpha =0.05=5\%$

The null hypothesis statement is that there is no connection between the variables, where the alternative hypothesis statement is that there is a connection between the variable.

  $H_0:$ There is no connection between smoking and Drinking.

  $H_1:$ There is a connection between smoking and Drinking.

The row and column totals are

The expected frequencies $E$

  $\begin{array}{c}{E}_{11}=\frac{r_1\times c_1}{n}=\frac{33\times 68}{177}=12.6780\\ E_{12}=\frac{r_1\times c_2}{n}=\frac{33\times 109}{177}=20.3220\\ E_{21}=\frac{r_2\times c_1}{n}=\frac{144\times 68}{177}=55.3220\\ E_{22}=\frac{r_2\times c_2}{n}=\frac{144\times 109}{177}=88.6780\end{array}$

The value of the test- statistic is

  $\begin{array}{c}{\chi }^2={\displaystyle \sum \frac{{\left(O-E\right)}^2}{E}}\\ =\frac{{\left(20-12.6780\right)}^2}{12.6780}+\frac{{\left(13-20.3220\right)}^2}{20.3220}\\ +\frac{{\left(48-55.3220\right)}^2}{55.3220}+\frac{{\left(96-88.6780\right)}^2}{88.6780}\\ =8.4405\end{array}$

The degree of freedom is.

  $df=(r-1)\left(c-1\right)=\left(2-1\right)\left(2-1\right)=1$

The P-Value is the probability of obtaining the value of the test statistic, or a value more extreme.

  $0.001<P<0.01$

(b)

To determine

To Explain: the conclusion from this study in plain language.

Explanation of Solution

If the P-value is equal or less than to the significance level, then the alternative hypothesis is accepted and null hypothesis is rejected:

  $P<0.05\Rightarrow {\text{Reject H}}_0$

There is not enough evidence to help the claim that there is a connection between smoking and drinking.