Chapter 11: Q. 30 (page 706)

The two-way table shows the results of the experiment described in
Exercise 28.
Hatching Status water temperature:cold water temperature:neutral
water temperature:hot
Total
Yes $16$
$38$
$75$
$129$
No $11$
$18$
$29$
$58$
Total
$27$
$56$
$104$
$187$
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

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	$27$	$56$	$104$	$187$

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 .

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	$27$	$56$	$104$	$187$

Part (b) Step 2:Explanation

The expected count is calculated as:

So, The expected count in Cold/Yes cell = $\frac{129 * 27}{187}$ = $18.62$

Table of expected counts :

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

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	$27$	$56$	$104$	$187$

Part (c) Step 2:Explanation

Here,

f_o=observed count

f_e=expected count

f_o	f_e	f_o-f_e	(f_o-f_e)²	(f_o-f_e)²/f_e
$16$	$18.62$	$- 2.62$	$6.86$	$0.36$
$11$	$8.37$	$2.63$	$6.91$	$0.82$
$38$	$38.63$	$- 0.63$	$0.39$	$0.01$
$18$	$17.36$	$0.64$	$0.40$	$0.02$
$75$	$71.74$	$3.26$	$10.62$	$0.14$
$29$	$32.25$	$- 3.25$	$10.56$	$0.32$
				Chi-Square value : $1.67$

Calculated chi-square value : $1.67$

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Short Answer

Step by step solution

Part (a) Step 1:Given Information

Part (a) Step 2:Explanation

Part (b) Step 1:Given Information

Part (b) Step 2:Explanation

Part (c) Step 1:Given Information

Part (c) Step 2:Explanation

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