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Chapter 11: Q. 30 (page 706)

The two-way table shows the results of the experiment described in

Exercise 28.

Hatching Statuswater temperature:coldwater temperature:neutral
water temperature:hot
Total
Yes16
38
75
129
No11
18
29
58
Total
27
56
104
187

a. State the appropriate null and alternative hypotheses.

b. Show the calculation for the expected count in the Cold/Yes 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 hatching status are not different for the three types of water temperature.

Alternative hyptheses: The hatching status are different for the three types of water temperature .

(b)The expected count in Cold/Yes cell =18.62

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

Step by step solution

01

Part (a) Step 1:Given Information

We have been given that,

Hatching Status
water temperature:cold
water temperature:neutral
water temperature:hot
Total
Yes
16
38
75
129
No
11
18
29
58
Total
27
56
104
187
02

Part (a) Step 2:Explanation

Null hyptheses:The hatching status are not different for the three types of water temperature.

Alternative hyptheses: The hatching status are different for the three types of water temperature .

03

Part (b) Step 1:Given Information

We have been given that,

Hatching Status
water temperature:cold
water temperature:neutral
water temperature:hot
Total
Yes
16
38
75
129
No
11
18
29
58
Total
27
56
104
187
04

Part (b) Step 2:Explanation

The expected count is calculated as:

So, The expected count in Cold/Yes cell = 129*27187=18.62

Table of expected counts :

Hatching Status
water temperature:cold
water temperature:neutral
water temperature:hot
Yes
18.62
38.63
71.74
No
8.37
17.36
32.25
05

Part (c) Step 1:Given Information

We have been given that,

Hatching Status
water temperature:cold
water temperature:neutral
water temperature:hot
Total
Yes
16
38
75
129
No
11
18
29
58
Total
27
56
104
187
06

Part (c) Step 2:Explanation

Here,

fo=observed count

fe=expected count

fo
fe
fo-fe
(fo-fe)2
(fo-fe)2/fe
16
18.62
-2.62
6.86
0.36
11
8.37
2.63
6.91
0.82
38
38.63
-0.63
0.39
0.01
18
17.36
0.64
0.40
0.02
75
71.74
3.26
10.62
0.14
29
32.25
-3.25
10.56
0.32




Chi-Square value :1.67

Calculated chi-square value :1.67

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