1.

a.  10 moneylenders were surveyed and asked to report the interest

rate they charged for a short term loan. The reported interest rates in percentages (%) are displayed below:

i.  Calculate the mean, median and mode for the interest rates charged [5 marks]

ii.   Using class intervals of 0-4.99, 5-9.99, 10-14.99 etc.,

construct a table showing frequencies and relative

frequencies of interest rates charged. Draw a diagram

showing the distribution of interest rates charged based on your table. [10 marks]

b.  The height (in centimetres) of boys aged five in a developing country is a random variable (X) that follows a Normal distribution with a

mean of 110cm and a standard deviation of 4cm. According to

Unicef, a child is stunted if its height is below 2 standard deviations of the mean.

Find the probability that a child is stunted. Sketch a graph to support your answer. [5 marks]

c.  The weight (in kilograms) of boys aged five in a high-income country is a random variable (X). The distribution of X is not known.

According to the World Health Organization, a child is underweight if its weight is below 2 standard deviations of the mean and overweight if its weight is above 2 standard deviations of the mean.

Find the maximum percentage of boys aged five who are over-

weight or under-weight. Explain your reasoning carefully and sketch a graph to support your answer. [10 marks]

2.

a.  The following pairs of scores were obtained from a random sample of 6 students who took  the Macroeconomics (Mac) and

Microeconomics (Mic) exams. The first score  is the Mac grade and the second the Mic grade.

(47, 57)  (40, 56)  (41, 40)  (32, 44) (69, 67)  (77, 70)

i.  Compute and interpret the Spearman Rank Order Correlation Coefficient for the Mac and Mic scores. [5 marks]

ii.   Using the answer you obtained in (i) above and a significance level of 0.05 test whether there is a significant correlation in    ranks across the exam scores for the two subjects. [5 marks]

iii.   Discuss under what circumstances the Spearman correlation coefficient would be preferred over the Pearson correlation    coefficient. [5 marks]

b.  The average daily outputs of 10 workers in company A are

compared to those of 10 workers in company B. The following data are obtained:

x̅A  = 420                                                               x̅B  = 408

SA  = 25                                                                  SB  = 20

i.  Conduct a hypothesis test to determine whether there is a     difference in variances between the two groups using a 0.05 level of significance. What do you conclude? [10 marks]

ii.   Using a 0.05 level of significance, undertake a hypothesis test to determine whether on average workers from company A

produce more per day than workers from company B.  What do you conclude? [10 marks]

3.

a.  It is  claimed that an average child spends 15 hours per week

watching television. A survey of 100 children finds an average of 14.5 hours per week, with a standard deviation of 8 hours.

Undertake a hypothesis test of the claim  using a 0.05  level of significance. [8 marks]

b.  From a sample of 150  Economics students at Manchester

university, 67% were found to have passed their Statistics test. From a sample of  120 Economics students at Sussex university, 62%

were found to have passed their Statistics test. Estimate the 99%   confidence interval for the true difference between the  proportions passing the exam. [8 marks]

c.  The daily output produced in three different factories (A, B, and C) is observed and reported to be as follows:

Is there a significant difference in output produced across the three factories at the 5% significance level? [10 marks]

d.  A random sample of 1000 people were asked to report their age and  preferred music category. The information is summarised in the table below.

Is there evidence at the 1% significance level that there is an

association between preferred music category and an individual's age? [9 marks]

4.  To  study  the  determinants  of  the  demand  for  margarine  the  following

regression equation was estimated using Ordinary Least Squares (OLS):

Margconsi = α + β1Margpricei + β2Butterpricei + β3Incomei + ui

where the variables are defined as follows:

Margcons represents the consumption of margarine in ounces per person per week;

Margprice represents the price of margarine in pence per 8 ounce pack;

Butterprice represents  the price of butter (a likely substitute for margarine) in pence per 8 ounce pack;

Income represents real income in £s;

ui is an error term.

The  regression results are presented below:

Regression Statistics              

a.  Interpret  the  estimated  coefficients  of  β1 , β2 ,  and β3   and  test  the statistical significance of each individual coefficient at the 5% level. State clearly the null and alternative hypotheses in each case. [10 marks]

b.  Test the overall significance of the regression at the 5% level. State the null and alternative hypotheses clearly. [10 marks]

c.  The following are the means of each variable:

Margcons   3.55

Margprice   110.62

Butterprice   110.57

Income   89.15