Question

More candy The two-way table shows the results of the experiment

described in Exercise 27.

	Red Survey	Blue Survey	Control Survey	Total
Red Candy	$13$	$5$	$8$	$26$
Blue Candy	$7$	$15$	$12$	$34$
Total	$20$	$20$	$20$	$60$

a. State the appropriate null and alternative hypotheses.

b. Show the calculation for the expected count in the Red/Red cell. Then provide a

complete table of expected counts.

c. Calculate the value of the chi-square test statistic.

Short answer

(a)Null hyptheses:The true distributions of color choice are not different for the three types of surveys.

Alternative hyptheses: The true distributions of color choice are different for the three types of surveys.

(b)The expected count in Red/Red cell =$8.67$

(c)The value of the chi-square test statistic =$6.62$

Step-by-step solution

Part (a) Step 1:Given Information

We have been given that,

	Red Survey	Blue Survey	Control Survey	Total
Red Candy	$13$	$5$	$8$	$26$
Blue Candy	$7$	$15$	$12$	$34$
Total	$20$	$20$	$20$	$60$

Part (a) Step 2:Explanation

Null hyptheses:The true distributions of color choice are not different for the three types of surveys.

Alternative hyptheses: The true distributions of color choice are different for the three types of surveys.

Part (b) Step 1:Given Information

We have been given that,

	Red Survey	Blue Survey	Control Survey	Total
Red Candy	$13$	$5$	$8$	$26$
Blue Candy	$7$	$15$	$12$	$34$
Total	$20$	$20$	$20$	$60$

Part (b) Step 2:Explanation

The expected count is calculated as:$\frac{RowTotal*ColumnTotal}{GrandTotal}$

So, The expected count in Red/Red cell =$\frac{26*20}{60}$=$8.67$$8.67$

Table of expected counts :

	Red Survey	Blue Survey	Control Survey
Red Candy	$8.67$	$8.67$	$8.67$
Blue Candy	$11.33$	$11.33$	$11.33$

Part (c) Step 1:Given Information

We have been given that,

	Red Survey	Blue Survey	Control Survey	Total
Red Candy	$13$	$5$	$8$	$26$
Blue Candy	$7$	$15$	$12$	$34$
Total	$20$	$20$	$20$	$60$

Part (c) Step 2:Explanation

Here,

f_o=observed count

f_e=expected count

fo	fe	fo-fe	(fo-fe)2	(fo-fe)2/fe
$13$	$8.67$	$4.33$	$18.74$	$2.16$
$7$	$11.33$	$-4.33$	$18.74$	$1.65$
$5$	$8.67$	role="math" localid="1654163603493" $-3.67$	$13.46$	$1.55$
$15$	$11.33$	$3.67$	$13.46$	$1.18$
$8$	$8.67$	$-0.67$	$0.44$	$0.05$
$12$	$11.33$	$0.67$	$0.44$	$0.03$
				Chi-Square value:$6.62$

Calculated chi-square value :$6.62$