QUESTION 1

The manager of a famous food outlet conducted a survey and took a sample of 13 customers’ spending at the salad bar during lunch time. The data is given below in terms of Rs spent at the salad Bar: 

298  562  492  266 512  631  1049  451  264  545  317  426   342

(a) (i) compute  mean, median and mode.

(ii) Looking at the division of the spending, which measure of location do you think is best and which one is worst? Why with reasons?

(b) Compute the first quartile, third quartile, range and interquartile range.

 (c) Compute the variance, standard deviation and the coefficient of variation. Interpret the result of the standard deviation.

 (d) Create a box and whisker plot. Are the data skewed? Justify your answer.

 (e) A manager informs his staff that a customer will spend “Almost certainly not more than Rs 500”. On the basis of results of (a) and (b), evaluate the accuracy of the statement.                                                                        

QUESTION 2

To examine the relationship between annual expenses on food and annual household disposable income, a sample of 1 000 households was taken and the following sums were calculated from sample data:-

Σx = 28 130

Σx² = 830 580

Σy = 23 450

Σy²= 560 536

Σxy = 676 871

Where y represents annual expenditure on food (in £ 000) and x represents annual household disposable income (in £ 000).

(i)  Utilize this sample information to calculate the mean and standard deviation of x and of y.                                                                                               

(ii) Taking annual outgoings on food as the dependent variable and household disposable income as the independent variable, calculate the equation of the least-squares regression line.                                                               

(iii) Compute the Pearson correlation coefficient between the two variables and comment on the result.                                                                              

(iv)  Expect the food expenditure of a household with an annual disposable income equal to £20 000. Remark on the likely accuracy of your prediction.         

QUESTION 3

 The manager of a hotel wants to learn characteristics of his customers. In particular he decides to focus on two variables: the amount of money spent by the customer and whether the customer would consider extending his stay. The results from a sample of 70 customers are as follows:

Amount Spent: Sample Mean = USD 1 759; s = USD 380.

42 customers stated that they would consider extending their stay.

(a) Set up a 99 percent confidence interval estimate of the population mean amount spent in the hotel.                                                                             

(b) Set up a 95 percent confidence interval estimate of the population proportion of customers who would consider extending their stay.                       

If a manager from another hotel wants to conduct a similar survey in his hotel (and does not have access to the information obtained by the manager of the first hotel); calculate the following:

(c) If he wants to have 95 percent confidence of estimating the true population mean amount spent in his hotel to within ±USD 10 and the standard deviation is assumed to be USD 50, what sample size is needed?                     

 (d) If he wants to have 90 percent confidence of estimating the population proportion of customers who staying in the hotel to be within ±0.04, what sample size is needed?                     

(e) Based on your answers to (c) and (d), what size sample must be taken?