Problem 1: A company wants to determine if customers have a preference for any of the following four brand of tea: A, B, C and D. From a random sample of 300 customers, it was found that 67 preferred A, 78 preferred B, 85 preferred C, and the remainder preferred D. Test the null hypothesis that customers have no preference for any of the four brands of tea.
Problem 2: The manager of a marketing research company wants to assess whether the customers' preference for any of the four brands of Ice-cream: A, B, C, and D is independent of their flavours: Vanilla, Chocolate, and Strawberry. A random sample of 527 customers was asked about their choice and the data are given in the following table:
A B C D
Vanilla 28 90 20 35
Chocolate 86 45 23 22
Strawberry 37 30 27 84
(a) Calculate the proportion of customers preferring Vanilla flavours.
(b) Calculate the proportion of customers preferring brand B
(c) What proportion of customers does prefer chocolate flavour of brand A?
(d) Which brand with Strawberry flavour has the highest proportions of customers? Justify your answer.
(e) Test the hypothesis that the customers' preference for any of the four brands of ice-cream is independent of their flavour. Use 5% significance level.
Problem 3: An instructor has a class of 23 students. At the beginning of semester, each student is randomly allocated to one of the four teaching assistants- Sam, Denniel, Michael, and Robert. The students are encouraged to meet with their assigned teaching assistant to discuss difficult course material. At the end of the semester, a common examination is administered. The score obtained by students working with these teaching assistants are shown in the accompanying table.
Sam Denniel Michael Robert
72.5 78.0 80.0 79.5
69.0 93.0 68.5 69.5
84.5 79.5 59.0 61.0
76.0 97.0 75.5 74.5
63.0 88.5 81.0 84.5
80.0 68.0 63.0
(a) Prepare the analysis of variance table for these data
Test the null hypothesis that students working under different teaching assistants performed equally in the exam