Bsc (Hons) Tourism and Hospitality Management. Resit Examinations for / Semester 2

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1 Bsc (Hons) Tourism and Hospitality Management Cohort / Year II - Part Time Resit Examinations for / Semester 2 MODULE: Introduction to Statistics MODULE CODE: THM2113 Duration: 2 Hours Reading time: 15 Minutes Instructions to Candidates: 1. This paper consists of two sections A and B 2. Section A is compulsory 3. Answer any two questions from section B 4. Electronic calculators can be used 5. All important steps in calculation must be shown This question paper contains 4 questions and 5 pages. Page 1 of 5

2 SECTION A: COMPULSORY QUESTION 1: (40 MARKS) a. Define and differentiate between: (i) nominal and ordinal data; and (ii) discrete and continuous data. (10 marks) b. A random sample of managing directors of hotels was selected. The bonuses, in Rs, paid to these managing directors had the following frequency distribution: Bonus to Managing Directors Number of managing directors 0 5, ,000 10, ,000 15, ,000,000 46,000 25, ,000 30, ,000 35, (i) Draw a histogram for the distribution and comment on its shape. (8 marks) (ii) Find the mean and standard deviation of the bonus paid to managing directors. (iii) If a manager is randomly selected, estimate the probability that a. He/she receive bonus in excess of Rs 30,000. (2 marks) b. He/she receive bonus between Rs 15,000 and 30,000. (2 marks) (iv) How many managing directors were selected in this sample? Describe how you would have selected this random sample. (v) Define non-probability sampling. Give two examples of non-probability sampling explaining clearly how it works. (7 marks) Page 2 of 5

3 SECTION B: ANSWER ANY TWO QUESTIONS QUESTION 2: (30 MARKS) An increasing number of holidaymakers are exploring the internet for savings in holiday accommodation. A sample of 400 travellers is selected. Suppose that a table of whether holidaymakers look for accommodation on the internet and find it more convenient to book accommodation on the internet revealed the following results: Find it comfortable to book Research accommodation accommodation on the internet on the Internet Yes No Yes No 100 a. If a holidaymaker is selected at random, what is the probability that: (i) he/she researches (2 marks) (ii) he/she is comfortable to book (2 marks) (iii) he/she researches accommodation and is comfortable to book (2 marks) (iv) he/she researches accommodation or is comfortable to book (4 marks) b. Suppose a randomly selected holidaymaker researches accommodation on the internet. What is the probability that he/she is comfortable to book c. Suppose a randomly holidaymaker employee is not comfortable to book accommodation on the internet. What is the probability that he/she does not research d. Explain the difference in the results of (b) and (c). (4 marks) e. Are researching accommodation on the internet and convenience to book accommodation on the internet statistically independent? Explain using probability. Page 3 of 5

4 QUESTION 3: (30 MARKS) A well-known company in the hotel and tourism business has branches in regions A, B, C, D and E. It wishes to undertake a survey of employee satisfaction across the entire company. The number of employee at each branch is given as follows: Office Number of employees Office Number of employees A 1900 D 250 B 350 E 300 C 100 F 100 Discuss how the sample could be undertaken, including the advantages and disadvantages of each method, if it is decided that the survey should be based upon: (a) A census (b) A 10% sample constructed for : (i) Simple random sampling. (ii) Stratified random sampling. (iii) Systematic sampling. (iv) Cluster sampling. (5 x 6 marks) Page 4 of 5

5 QUESTION 4: (30 MARKS) a. What is meant by Type I and Type II errors? (7 marks) b. A sample of employees in the front office of a hotel was selected. Each employee was asked to describe: (i) his/her own job satisfaction (X), on a scale of 1 to 10, and (ii) the number of days of overtime (Y) during the previous month. The above information was summarized as follows: X = 31 =. 2 i Y i X 2 = = i Y i i= 1 X Y i i = 65.5 (i) Estimate the linear regression for the number of days the employees are absent from work during the last year. (8 marks) (ii) State the simple linear regression equation and interpret the meaning of the slope (4 marks) (iii) Given that three employees has job satisfaction level 4, 7 and 12, predict the average number of days this employee would work as overtime. (iv) Estimate the correlation coefficient. ***END OF QUESTION PAPER*** Page 5 of 5