Chapter 10.1, Problem 10.16E

(a)

To determine

To Explain: the null and alternative hypotheses for the question of interest.

Answer to Problem 10.16E

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

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

Explanation of Solution

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 variables.

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

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

(b)

To determine

To Calculate: the expected counts.

Answer to Problem 10.16E

	Smoked	did not smoke
Yes	$12.6780$	$20.3220$
No	$55.3220$	$88.6780$

Explanation of Solution

Formula used:

  $E=np$

Calculation:

Row and column total is

	Smoked	did not smoke	total
Yes	20	13	20+13=33
No	48	96	48+96=144
Total	20+48=68	13+96=109	33+144=177

The expected frequencies are

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