Introduction to Hypothesis Testing

Question 1

Hypothesis

Answer 1

is a conjecture about a population
parameter. This conjecture may or may
not be true.

Question 2

Two Types of Hypothesis

Answer 2

1. Null Hypothesis
2. Alternative Hypothesis

Question 3

Two Types of Hypothesis

Answer 3

1. Null Hypothesis
2. Alternative Hypothesis

Question 4

Null Hypothesis

Answer 4

symbolized by 𝑯𝟎, is a statistical hypothesis
that states that there is no difference
between a parameter and a specific value, or
that there is no difference between two
parameters.

Question 5

Alternative Hypothesis

Answer 5

symbolized by 𝑯𝒂 (or 𝑯𝟏 ), is a statistical
hypothesis that states the existence of a
difference between a parameter and a specific value, or states that there is a difference between two parameters.

Question 6

Three Methods in Hypothesis Testing

Answer 6

1. The traditional method
2. The 𝑃-value method
3. The confidence interval method

Question 7

Null Hypothesis (𝐻0)

Answer 7

is the statement being
tested.

Question 8

Alternative Hypothesis (𝐻a )

Answer 8

possible values
about the population parameter.

Question 9

𝑯𝒂∶ 𝝁𝟏 ≠ 𝝁2

Answer 9

(two-tailed test)

Question 10

𝑯𝒂 ∶ 𝝁𝟏 > 𝝁2

Answer 10

(one-tailed test)

Question 11

𝑯𝒂 ∶ 𝝁𝟏 < 𝝁2

Answer 11

(one-tailed test)

Question 12

Basic Steps in the Traditional Hypothesis Testing

Answer 12

1.Formulate the Null and Alternative Hypothesis
2. Set the Level of Significance (𝜶)
3. Determining the Statistical Test to be Used
4. Data Computation
5. Determining the Acceptance and Rejection Regions
6. Compare the computed / test value and the
critical / tabular value obtained
7. State your decision and conclusion.

Question 13

Types of Test Used with the Alternative Hypothesis

Answer 13

a. One-Tailed Test
b. Two-Tailed Test

Question 14

One-Tailed Test

Answer 14

Used when the rejection region is located at only one extreme of the range value of the test statistic, or it occupies only one side of the normal curve.

Question 15

One-Tailed Test

Answer 15

It is located only in one tail of the distribution in the rejection region; either in the left tail or the right tail of the distribution of the test statistic with an associated area of 𝛼 which also indicates a directional hypothesis.

Question 16

Two-Tailed Test

Answer 16

a test which locates its critical region on both
tails of the distribution which also indicates a
Non-directional Hypothesis.

Question 17

Level of Confidence

Answer 17

• “belief”
• the degree of assurance that a particular statistical statement is correct under specified conditions
• represents the probability that 𝐻0 is true

Question 18

Level of Significance

Answer 18

• “doubt”
• the degree of uncertainty about the statistical statement under the same conditions used to determine the confidence level
• represents the probability that 𝐻𝑜 is false

Question 19

The most commonly used values of 𝛼 are 0.01, 0.05 and 0.10. Choosing 0.01 level of significance means that the researcher is 99% confident and has 1% to
commit an error.

Answer 19

The most commonly used values of 𝛼 are 0.01, 0.05 and 0.10. Choosing 0.01 level of significance means that the researcher is 99% confident and has 1% to
commit an error.

Question 20

TYPES OF ERROR

Answer 20

Type I
Type II

Question 21

Type I

Answer 21

Reject 𝐻0 while it is true

Question 22

Type II

Answer 22

Accept 𝐻0 while it is false

Question 23

statistical test

Answer 23

uses the data obtained from a
sample to make a decision about whether the null hypothesis should be rejected.

Question 24

test value or test statistic

Answer 24

The numerical value obtained from a statistical test

Question 25

Statistical Tests

Answer 25

a. 𝒛-Test
b. 𝒕-test

Question 26

𝒛-Test

Answer 26

Basic Assumptions:
- the sample is a random sample
- population standard deviation (𝜎) is known
- either 𝑛 ≥ 30 or the population is normally
distributed if 𝑛 < 30
One-sample 𝒛 −Test

Question 27

𝒕-test

Answer 27

Basic Assumptions:
- the sample is a random sample
- population standard deviation (𝜎) is unknown (sample standard deviation (𝑠) is given instead)
- either 𝑛 ≥ 30 or the population is normally
distributed if 𝑛 < 30

Question 28

critical value

Answer 28

separates the critical region from the
noncritical region

Question 29

critical / rejection region

Answer 29

is the range of values of
the test value that indicates that there is a significant difference and that the null hypothesis should be rejected

Question 30

noncritical / nonrejection / acceptance region

Answer 30

is the range of values of the test value that indicates that the difference was probably due to chance and that the null hypothesis should not be rejected

Question 31

If the absolute computed value of the test statistic is less than the absolute critical / tabular value,

Answer 31

accept the null hypothesis and reject the alternative hypothesis.