Question

A major food manufacturer is concerned that the sales for its skinny french fries have been decreasing. As a part of a feasibility study, the company conducts research into the types of fries sold across the country to determine if the type of fries sold is independent of the area of the country. The results of the study are shown in the table. Conduct a test of independence.

Type of Fries	Northeast	South	Central	West
skinny fries	70	50	20	25
curly fries	100	60	15	30
steak fries	20	40	10	10

a. Test Statistic:

b. accept or reject:

Answer 1

hypothesis:-

the type of fries sold and the area of the country are independent.

the type of fries sold and the area of the country are dependent.

here, we will do chi square test for independence.

necessary calculation table:-

		the area of the country
		northeast	south	central	west	row total
skinny fries	observed freq(Oi)	70	50	20	25	165
	expected freq(Ei)	(165*190)/450=69.666	55	16.5	2.8333
		0.0016	0.4545	0.7424	0.0571	1.2556
curly fries	observed freq(Oi)	100	60	15	30	205
	expected freq(Ei)	86.5556	68.3333	20.5	29.6111
		2.0883	1.0163	1.4756	0.0051	4.5853
steak fries	observed freq(Oi)	20	40	10	10	80
	expected freq(Ei)	33.7778	26.6667	8	11.5556
		5.6199	6.6667	0.5	0.2094	12.996
column total		190	150	45	65	450

a). test statistic be:-

b). p value = 0.0044

[ df = (4-1)*(3-1) = 6

in any blank cell of excel type =CHISQ.DIST.RT(18.8369,6) press enter]

decision:-

p value = 0.0044 < 0.05

so, we reject the null hypothesis.

conclusion:-

there is not sufficient evidence to claim that  the type of fries sold is independent of the area of the country at 0.05 level of significance.

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