MDA5201  MATHEMATICAL STATISTICS AND DATA ANALYSIS  KCA Past Paper

UNIVERSITY EXAMINATIONS: 2018/2019
EXAMINATION FOR THE DEGREE OF MASTERS OF SCIENCE IN
DATA ANALYTICS
MDA5201 MATHEMATICAL STATISTICS AND DATA ANALYSIS
PART-TIME/ WEEKEND
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?
[2 Marks]
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]
iii. Find

[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.
[5 Marks]
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:
Descriptive Statistics
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
[4 Marks]
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?
[3 Marks]
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]

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