Question

Introduction to Statistical Modelling Monday, Feb. 25, 2019 Part II. 7 Long-answer questions; Give the solutions for the following questions in details. Suppose 510 people selected at random to rate Hotel ABC according to price (low, medium, or high) and quality (one, two, three, or four stars). The results are presented in the following contingency table, the numbers represent frequencies. 1 Star 2 Stars 3 Stars 4 Stars Total 90 95 40 225 160 Low 20 Medium 50 15 25 250 30 100 70 35 80 High 25 5 Total 95 120 510 If a client from hotel ABC is randomly selected. (a) (3 pts) Find the probability that the person rates the prices medium (b) (3 pts) Find the probability that the person rated the quality two stars (c) (3 pts) Suppose the person selected the high price, what is the probability that he rates the quality as one star? (d) (4 pts) Suppose the person does not select the four stars quality, what is the prob- ability that he rates the prices high?

Answer 1

A1) a) P( rate the prices medium) = 215/510 = 0.4216

B) P(rated the quality = 120/510 = 0.2353

C) P(rate the quality as one star | high price) = 25/100 = 0.25

D) P(rates the prices high | doesn't select the four stars quality) = (100 - 30)/(510 - 70)

= 70/440 = 0.1591