Question

Each year the Hershey company reviews candy bar sales records to compare current consumer preferences to sales records of previous years. Previous sales suggest that 30% of consumers prefer Kit Kats, 15% prefer PayDays, 5% prefer the Whatchamacallit, and 50% prefer the traditional Hershey’s chocolate bar. Market analysts collect a sample of consumers from a random day 2018 and found that 50 people preferred Kit Kat, 45 people prefer PayDay, 12 people prefer Whatchamacallits, and 93 people prefer the traditional Hershey chocolate bars. Have current preferences changed from the historical preferences?

(please also specify null and alternative hypothesis)

Answer 1

null hypothesis: current preferences are same as stated proportion in previous sales

Alternate hypothesis: current preferences have change from stated proportion in previous sales

degree of freedom =categories-1=			3
for 0.05 level and 3 df :crtiical value X2 =				7.815
Decision rule: reject Ho if value of test statistic X2>7.815
applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.3000	50.0000	60.00	-1.29	1.667
2	0.1500	45.0000	30.00	2.74	7.500
3	0.0500	12.0000	10.00	0.63	0.400
4	0.5000	93.0000	100.00	-0.70	0.490
total	1.000	200	200		10.0567
test statistic X2 =		10.057

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that current preferences have changed from the historical preferences