Lecture 5 (STATISTICAL INFERENCE 1)

Question 1

HYPOTHESIS TESTING

Answer 1

Researchers are able to structure problems in such a way that the researcher can use statistical evidence to test various theories about phenomena.

Question 2

RESEARCH HYPOTHESIS

Answer 2

A statement of what the researcher believes will be the outcome of an experiment or a study.

Question 3

STATISTICAL HYPOTHESES

Answer 3

A more formal structure derived from the research hypothesis.
Composed of two parts:
Null Hypothesis (Ho): null hypothesis exists; old statement is correct. 
Alternative (Ha): the new theory is true

Question 4

SUBSTANTIVE HYPOTHESES

Answer 4

A statistically significant difference does not imply or mean a material, substantive difference.
If the null hypothesis is rejected and the alternative hypothesis is accepted, then one can say a statistically significant result has been obtained.
With “significant” results you reject the null hypothesis.

Question 5

NULL HYPOTHESIS

Answer 5

Ho

Nothing new is happening; the null condition exists.

Question 6

ALTERNATIVE HYPOTHESIS

Answer 6

Ha

Something new is happening.

Question 7

Features of the null and alternative hypotheses.

Answer 7

They are mutually exclusive, only one can be true.
Collectively exhaustive.
The null hypothesis is assumed to be true.
The burden of proof falls on the alternative hypothesis.

Question 8

HTAB System to test hypotheses.

Answer 8

TASK 1: hypothesise
-Establish hypotheses: state the null and alternative hypothesis
TASK 2: TEST
-Determine the appropriate statistical test and sampling distribution
-Specify the Type 1 error rate (ɑ)
-State the decision rule
-Gather sample data
-Calculate the value of the test statistic
TASK 3: TAKE STATISTICAL ACTION
-Make the statistical conclusion
TASK 4: DETERMINING THE BUSINESS IMPLICATIONS.
- Make a managerial decision.

Question 9

REJECTION REGION

Answer 9

Conceptually and graphically, statistical outcomes that result in the rejection of the null hypothesis lie in what is termed the rejection region..

Question 10

NON-REJECTION REGION

Answer 10

Statistical outcomes that fail to result in the rejection of the null hypothesis lie in what is termed the non-rejection region.
Tails of normal distribution.

Question 11

TYPE I ERROR

Answer 11

Committed by rejecting a true null hypothesis.
If the null hypothesis is true, any mean that falls in a rejection region will be a type 1 error.
The probability of committing a Type 1 error is called ɑ, the level of significance.

Question 12

TYPE II ERROR

Answer 12

Committed when a researcher fails to reject a false null hypothesis.
The probability of committing a Type II error is called β.

Question 13

ONE TAILED TESTS

Answer 13

H0 : u = 40
        u < 40
OR
H0 : u = 40
        u > 40

Question 14

TWO TAILED TESTS

Answer 14

H0 : u = 40

u ≠ 40

Question 15

When can the z formula be used to test hypothesis?

Answer 15

About a single population mean if the sample size (n) is > 30 for any population, and < 30 if x is normally distributed.

Question 16

How is the p value used to test hypothesis?

Answer 16

Using the p-value is another way to reach statistical conclusion in hypothesis testing.
No preset value of ɑ is given.
P value defines the smallest value of ɑ for which the null hypothesis can be rejected.

p-value < ɑ reject H0
p-value ≥ ɑ do not reject H0

Question 17

How is the p value used to test hypothesis in a two tailed test?

Answer 17

Alpha is split to determine the critical value of the test statistic.
With the p value, the probability of getting a test statistic at least as extreme as the observed value is computed.
The p value is then compared z or α/2 for two tailed tests to determine statistical significance.

Question 18

CRITICAL VALUE METHOD TO TEST HYPOTHESES

Answer 18

The critical value method determines the critical mean value required for z to be in the rejection region and uses it to test the hypotheses.

z = (xbar - u) / (o / sqrt(n))

e.g.
+/- 1.96 = (xbar - 74,914) / (14,530 / sqrt (112))

Question 19

TESTING HYPOTHESES ABOUT A POPULATION USING THE T STATISTIC (O UNKNOWN)

Answer 19

t = (xbar - u) / (s/sqrt(n))
df = n-1