Question

Question 6 (a) A hospital cafeteria proposes to serve 4 main entrees. For planning purposes, the manager expects that the proportions of each that will be selected by his customers will be: Selection Proportion Chicken 0.4 Roast beef 0.2 Steak 0.1 Fish 0.3 Of the first 100 customers, 44 selected chicken, 25 selected roast beef, 13 select steak, and 18 selected fish. Should the manager revise his estimates? Use α= 0.01.

(b) Five brands of orange juice are displayed side by side in several supermarkets in Hobart. It was noted that in one day, 180 customers purchased orange juice. Of these, 30 picked Brand A, 40 picked Brand B, 25 picked Brand C, 35 picked Brand D, and 50 picked Brand E. In this city, can you conclude at the 5% significance level that there is a preferred brand of orange juice? (9 marks

Answer 1

Answer (A)-

The null and alternative hypotheses are,

H0: The manager shouldn't revise his estimates,

i.e. p1​ = 0.4, p2​ = 0.2, p3​ = 0.1, p4​ = 0.3

Ha: The manager should revise his estimates, i.e. at least one of

the proportions differs significantly from that expected.

The level of significance, α = 0.01

The test statistic, χ2 = 7.350

The degrees of freedom = 3

The p-value = 0.0615

Since the p-value = 0.0615 > 0.01, do not reject the null hypothesis.

The results indicate no enough evidence to support the claim that

the manager revise his estimates

Answer (B)-