Business Research and Analytics

Time Constrained Assignment for

Business Research and Analytics

NOTE:  YOU MUST RETURN THIS QUESTION PAPER WITH YOUR ANSWER BOOK.

 

EXAM TIME: ONE HOURS

***ATTEMPT ALL QUESTIONS***

 

THERE ARE 25 MARKS FOR EACH QUESTION

 

YOU MAY USE TWO SIDES OF AN A4 PAPER-BASED REFERENCE MATERIALS THAT YOU HAVE BROUGHT WITH YOU.

 

CALCULATORS MAY BE USED AT THE DISCRETION OF THE EXAMINER PROVIDED THEY ARE NOISELESS, CORDLESS, NOT PRE-PROGRAMMED BY THE CANDIDATE AND CANNOT RECEIVE OR TRANSMIT DATA REMOTELY.

 

Question 1

The table below shows the Total Number (’00,000s) of Tourists and the Number (’0,000s) of Passenger Journeys made by these tourists on public transport in a city for a period of 10 years.

 

Year	1	2	3	4	5	6	7	8	9	10
Tourists (’00,000s) –  x	Table of Contents 7	13	15	10	12	8	9	10	12	9
Journeys (’0,000s)  –  y	21	19	37	32	31	25	23	24	29	22

 

• Plot a scatter diagram to display this data and comment briefly on what it shows.

          (8 marks)

• Given that Sx = 105, Sy = 263, Sx² = 1157, Sy² = 7211 and Sxy = 2834 find
• the correlation co-efficient between Number of the Tourists and Number of Journeys. Comment on the correlation coefficient.

(9 marks)

• the regression line used to predict the number of Journeys from the number of Tourists. Explain the use and importance of regression analysis for the organisation.

(8 marks)

Question 2

 

A company sells, amongst other products, a medicated shampoo.  The shampoo is sold in container sizes that are labeled as containing 500 ml.  The volume of liquid that is actually put into the containers is normally distributed with a mean of 510 ml and a standard deviation of 10 ml.

 

(a)       Estimate the probability that a container chosen at random will hold

 

(i)        more than 520 ml                                                                               (7 marks)

(ii)       between 495 ml and 515 ml                                                               (10marks)

(iii)      less than the advertised amount                                                          (8 marks)

 

 

 

 

Question 3

 

The table below shows the frequency distribution of the percentage rate of inflation for each of 100 countries.

 

% Inflation                   Frequency

 

0 to under 5                           37

5 to under 10                         25

10 to under 15                                    12

15 to under 25                                    11

25 to under 45                                     9

45 to under 100                        6

 

 

(a) Use this data to estimate the mean and standard deviation and variance of inflation rate.

(b) Comment on mean and standard deviation.

(c) Reflect on class distribution and adjust the classes as necessary.

(d) Comment on the distribution.

(e) Represent the data graphically using a histogram and estimate the mode of the distribution from the histogram

 

Question 4

 

Before a sales promotion campaign 10% of all sales points in a particular company were considered to be under performing.  After the campaign a random sample of 60 sales points was chosen and, of these, 4 were still under performing.  Is there evidence that the campaign has reduced the proportion of sales points that are under performing?  Carefully state the null and alternative hypotheses that you are using. (Use a 5% of significance level)