National Teachers’ Institute Kaduna (Post Graduate Diploma in Education) PDE 710 Statistical Methods in Education 2016

1. (a) Describe sampling (b) Explain any four (4) of its significance

2. (a) Distinguish between Type I and Type II error (b) Define Kurtosis

(c) With the aid of diagram, explain the following:

i. Leptokurtic

ii. Platykurtic

iii. Mesokurtic

3. (a) What is population of a study?

(b) Explain the following sampling techniques

i. Random sampling

ii. Stratified sampling

iii. Cluster Sampling sampling

4. (a) Differentiate between Parametric and Non-parametric statistics

(b) Give any four examples of each

5. Consider the table below and answer the questions that follow Class interval

F

201-400

401-600

601-800

1

2

5

801-1000

1001-1200

12 17

20

12

1201-1400)

1401-1600 1601-1800

7

3

1

1801-2000

Find,

2001-2200

A. The lower limit of the 4th class

B. The upper limit of the 5th class

C. The class mark of the 3rd class

D. The class boundaries of the 8th class

E. The size of the 6th class

1. (a) Sampling refers to the process of selecting a subset of individuals or items from a larger population in order to make inferences about the entire population.
(b) Four significances of sampling are:
– Cost-effectiveness: Sampling reduces the resources needed compared to studying the entire population.
– Time efficiency: Sampling allows quicker data collection and analysis.
– Feasibility: When the population is large or inaccessible, sampling becomes practical.
– Accuracy: Well-designed sampling can provide accurate and representative results.

2. (a) Type I error (False Positive) occurs when a true null hypothesis is rejected. Type II error (False Negative) occurs when a false null hypothesis is not rejected.
(b) Kurtosis is a statistical measure that indicates the degree of peakedness or flatness of a distribution compared to a normal distribution.

(c) Unfortunately, I’m unable to provide diagrams, but I can explain the terms:
– Leptokurtic: A distribution with higher peak and heavier tails than a normal distribution.
– Platykurtic: A distribution with lower peak and lighter tails than a normal distribution.
– Mesokurtic: A distribution with a peak and tail shape similar to a normal distribution.

3. (a) The population of a study refers to the entire group that researchers are interested in.
(b) Explanation of sampling techniques:
– Random Sampling: Every member of the population has an equal chance of being selected.
– Stratified Sampling: Dividing the population into subgroups (strata) and then randomly sampling from each stratum.
– Cluster Sampling: Dividing the population into clusters, then randomly selecting some clusters and sampling all individuals within those clusters.

4. (a) Parametric statistics make assumptions about the population distribution, while non-parametric statistics do not rely on specific distribution assumptions.
(b) Examples of parametric statistics: t-tests, ANOVA, linear regression, etc.
Examples of non-parametric statistics: Mann-Whitney U test, Wilcoxon signed-rank test, Kruskal-Wallis test, etc.

5. Here are the requested answers based on the table:
A. Lower limit of the 4th class: 801
B. Upper limit of the 5th class: 1200
C. Class mark of the 3rd class: 700
D. Class boundaries of the 8th class: 1800.5 – 2000.5
E. Size of the 6th class: 200