# Fundamentals of hypothesis testing: one-sample tests Flashcards

1
Q

Hypothesis

A

A hypothesis is a statement (assumption) about a population parameter

2
Q

Population mean example

A

Example: The mean monthly mobile phone bill of this city is μ = \$72

3
Q

Population proportion example

A

Example: The proportion of adults in this city with mobile phones is ∏ = 0.89

4
Q

The Null Hypothesis, H0

A

States the belief or assumption in the current situation (status quo)

Begin with the assumption that the null hypothesis is true
(similar to the notion of innocent until proven guilty)

Refers to the status quo

Always contains ‘=‘, ‘≤’ or ‘’ sign

May or may not be rejected

Is always about a population parameter; e.g. μ, not about a sample statistic

5
Q

The Alternative Hypothesis, H1

A

Is the opposite of the null hypothesis
e.g. The average number of TV sets in Australia
homes is not equal to 3 ( H1: μ ≠ 3 )

Challenges the status quo

Can only can contain either the ‘’ or ‘≠’ sign

May or may not be proven

Is generally the claim or hypothesis that the researcher is trying to prove

6
Q

Hypothesis testing process

A

PHOTOS 1-2

7
Q

The Level of Significance, alpha

A

hypothesis is true
Defines rejection region of the sampling distribution

Is designated by alpha, (level of significance)
Typical values are 0.01, 0.05, or 0.10
Note relationship to 99%, 95% and 90% confidence levels

Is selected by the researcher at the beginning

Provides the critical value(s) of the test

8
Q

Level of Significance and the Rejection Region

A

PHOTO 3

9
Q

Errors in making decisions

A

Type I error
Reject a true null hypothesis
Considered a serious type of error

Type II error
Fail to reject a false null hypothesis

10
Q

The probability of errors

A

The probability of Type I error is alpha
Called level of significance of the test; i.e. 0.01, 0.05, 0.10
Set by the researcher in advance

The probability of Type II error is β

11
Q

Outcomes and probabilities of hypothesis testing

A

PHOTO 4

12
Q

Z Test of Hypothesis for the Mean (σ Known)

A

PHOTO 5

13
Q

Critical Value Approach to Testing

A

For a two-tail test for the mean, σ known:
Convert sample statistic ( ) to the test statistic (Z statistic)
Determine the critical Z values for a specified level of significance  from a Table E.2 or computer
Decision Rule: If the test statistic falls in the rejection region, reject H0 ; otherwise do not reject H0

14
Q

Two tail tests

A

PHOTO 6

15
Q

6 STEPS IN HYPOTHESIS TESTING

A

State the null hypothesis, H0 and the alternative hypothesis, H1

Choose the level of significance, alpha, and the sample size, n

Determine the appropriate test statistic and sampling distribution

Determine the critical values that divide the rejection and non-rejection regions

Collect data and calculate the value of the test statistic

Make the statistical decision and state the managerial conclusion

16
Q

Step 6 expanded

A

if the test statistic falls into the non-rejection region, do not reject the null hypothesis H0; if the test statistic falls into the rejection region, reject the null hypothesis

express the managerial conclusion in the context of the real-world problem

17
Q

Hypothesis testing example

A

photos 7-10

18
Q

p-value approach to testing

A

p-value: Probability of obtaining a test statistic more extreme
( ≤ or ) than the observed sample value, given H0 is true

Also called observed level of significance
Smallest value of  for which H0 can be rejected
Obtain the p-value from Table E.2 or computer
If p-value < alpha , reject H0
If p-value >= alpha , do not reject H0

19
Q

p value example

A

Photos 11-12

20
Q

Connection to confidence intervals

A

Photo 13

21
Q

One tails tests

A

Photo 14

22
Q

Lower tail tests

A

Photo 15

23
Q

Upper tail tests

A

Photo 16

24
Q

Upper tail test example

A

Photos 17-20

25
Q

Upper tail test p-value example

A

Photo 21

26
Q

t test of hypothesis for the mean (sigma unknown)

A

Photo 22

27
Q

t test of hypothesis for the mean (sigma unknown) example

A

Photos 23-24

28
Q

Hypothesis Tests for Proportions

A

Photos 25-26

29
Q

Hypothesis Tests for Proportions example

A

Photos 27-28

30
Q

The power of a test (1 – β)

A

Photo 29

31
Q

Type II Error

A

Photos 30-31

32
Q

Pitfalls and Ethical Considerations

A

Use randomly collected data to reduce selection biases or coverage errors

Do not use human subjects without informed consent

Choose the level of significance, α, and the type of test (one-tail or two-tail) before data collection

Do not employ ‘data snooping’ to choose between one-tail and two-tail test, or to determine the level of significance

Do not practice ‘data cleansing’ to hide observations that do not support a stated hypothesis

Report all pertinent findings

Distinguish between statistical significance vs. practical significance