MGEB12H3 Study Guide - Midterm Guide: Type I And Type Ii Errors, Statistical Parameter, Confidence IntervalExam
DepartmentEconomics for Management Studies
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MGEB12: Quantitative Methods in Economics-II
Common Questions (Test-1)
Question-1: I am confused! How can I identify which is the null which is the alternative:
Answer: There are several ways to identify the null and the alternative:
Conceptual methods of identifying the null and the alternative:
a) The null is the status quo (what has been the case), the alternative is the departure from the status quo. As
a result, the null is assumed to be true but your intention is to reject it and to conclude that a change has
happened (i.e. the alternative is correct).
b) Following (a), typically a claim by manufacturers or institutions with regard to their products and/or
services is the null.
Mechanical methods in identifying the null and the alternative
a) The null has “=” sign while the alternative never has “=” sign. Therefore, statements that include “at least”
or “at most”, or equal are identifying the null while statements include, less, or different are identifying
Example-1: There is a claim that at least 25% of students achieve A in MGEB12:
(H0: P ≥ 0.25, H1: P < 0.25) which we can (and will most often) write as (H0: P = 0.25, H1: P < 0.25)
Example-2: An adoption of a new teaching method at UTSC has increased the average mark beyond
historical average of 70.
(H0: µ ≤ 70, H1: µ > 70) which we can (and will most often) write as (H0: µ = 70, H1: µ > 70).
b) The evidence we bring i.e. our sample statistics (sample means, sample proportion, …) are to reject the
null and to conclude the alternative. Therefore, in a directional test (upper tail, lower tail) the sample
statistics should point towards the alternative:
This means that in the upper tail test, the sample mean (sample proportion) has to be higher than the
population parameter in the null. i.e. your test statistics (Z or t) must be > 0.
This means that in the lower tail test, the sample mean (sample proportion) has to be lower than the
population parameter in the null. i.e. your test statistics (Z or t) must be < 0.
Question-2: I don’t understand the difference between Type-I error, and Type- II error. Which is a more serious
Type-I error: Rejecting the null if the null if correct.
Type-II error: Not rejecting the null if the alternative is correct (Null is incorrect)
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