UNIVERSITY EXAMINATIONS: 2018/2019
EXAMINATION FOR THE DEGREE OF MASTERS OF SCIENCE IN
MDA5201 MATHEMATICAL STATISTICS AND DATA ANALYSIS
DATE: DECEMBER, 2018 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One & ANY OTHER TWO questions.
QUESTION ONE: (20 MARKS)
a) Define each of the following statistical terms/concepts
i. Significance level [2 Marks]
ii. Statistical power [2 Marks]
iii. Parameter [2 Marks]
iv. Random assignment [2 Marks]
v. Effect size [2 Marks]
b) Suppose X is uniformly distributed in the range 0 to 1. What is the mean of X?
c) Suppose that x is a binomial random variable with n = 5 and p = 0.5.
i. For each value of x, calculate p(x) and construct a probability distribution table
for this phenomenon. [2 Marks]
ii. Sketch an histogram for this distribution [2 Marks]
iv. Find the expected value of x [2 Marks]
QUESTION TWO: (15 MARKS)
Suppose scores on the 2018 KCPE examinations were known to be normally distributed with
mean 300 and variance 3600. For a survey of standard 8th leavers in the country, a random
sample of size 900 is selected. Find,
(a) The standard deviation (otherwise known as standard error) of the mean KCPE score
originating from this sample. [4 Marks]
(b) The probability that the mean KCPE score from this sample will (i) fall between 280 and
305 (ii) be greater than 304. [6 Marks]
(c) Find the number of additional subjects needed to double the precision of this estimate.
QUESTION THREE: (15 MARKS)
In a study to assess the impact of mobility on standard seven students’ mathematics achievement, the
following descriptive statistics were obtained from SPSS:
Dependent Variable: Mathematics Score
State the null hypothesis for the study [2 Marks]
b. Name one statistical analytic technique you can use to test the hypothesis in (a) above
c. Test the hypothesis in (a) at the 0.05 level of significance. Include the critical value, the
observed test statistic, the decision rule, and your decision. [5 Marks]
d. In a sentence or two, write the interpretation of the findings in (c) [4 Marks]
QUESTION FOUR: (15 MARKS)
a. The correlation matrix below represents the relationship in the investment returns among
four portfolios (A, B, C, and D).
Describe the relationship among the four portfolios. [2 Marks]
ii. Suppose an investor intends to diversify his/her investment for optimum stability.
In which two portfolios can he/she invest to achieve this objective? Why?
b. Using the data below,
i. Sketch a scatterplot for the relationship between X and Y. [3 Marks]
ii. Describe the relationship between X and Y. [3 Marks]
iii. Compute the covariance of X and Y. [4 Marks]