Chapter 11.1, Problem 20E

To determine

To find chi square statistic.

Answer to Problem 20E

The chi square statistic is 10.80

Explanation of Solution

Given:

Type of food	Ramen	Tacos	Pizza	Hamburgers
Count	18	22	39	21

Null and alternative hypotheses:

  $H_0:p_R=p_T=p_P=p_H=0.25$

  $H_a:Atleastoneofthe{p}_i’sisincorrect.$

Using excel,

Type of food	observed	expected	O - E	(O - E)² / E	% of chisq
Ramen	18	25.000	-7.000	1.960	18.15
Tacos	22	25.000	-3.000	0.360	3.33
Pizza	39	25.000	14.000	7.840	72.59
Hamburgers	21	25.000	-4.000	0.640	5.93
Total	100	100.000	0.000	10.800	100.00
	10.80	chi-square
	3	df
	.0129	p-value

This calculation is same as option a. Hence, option a is correct.