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Chapter 11: Q. 29 (page 753)

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

described in Exercise 27.


Red SurveyBlue Survey
Control Survey
Total
Red Candy13
5
8
26
Blue Candy
7
15
12
34
Total20
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

Expert verified

(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

01

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
02

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.

03

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
04

Part (b) Step 2:Explanation

The expected count is calculated as:RowTotal*ColumnTotalGrandTotal

So, The expected count in Red/Red cell =26*2060=8.678.67

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
05

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
06

Part (c) Step 2:Explanation

Here,

fo=observed count

fe=expected count

fofefo-fe(fo-fe)2(fo-fe)2/fe
13
8.67
4.33
18.74
2.16
711.33
-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

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