Book 1_Quan_Hypothese testing

Question 1

• The hypothesis testing process

Answer 1

requires a statement of a null and an alternative hypothesis

Question 2

• The null hypothesis

Answer 2

is what the researcher wants to reject.

Question 3

• The alternative hypothesis

Answer 3

is what the researcher wants to support

Question 4

• The hypothesis testing principal

Answer 4

o Nếu test X = U, => Ho = U, Ha khác U
o Nếu test X >= U => Ho < U, Ha >= U
o Test statistic = (sample statistic – hypothesized value)/standard error of the sample statistics
o (X-U)/sample error
o Nguyên tắc cùng dấu: Test statistic cùng dấu với Ho hoặc Ha thì cái đó đúng
o U = Uo => Reject khi T < lower critical hoặc > higher critical

Question 5

sample statistic

Answer 5

the sample mean

Question 6

the standard error of the
sample statistic for sample size n

Answer 6

Standard error = population standard deviation/ can (n)

Question 7

Type I error

Answer 7

the rejection of the null hypothesis when it is actually true

Question 8

Type II error

Answer 8

the failure to reject the null hypothesis when it is actually false

Question 9

• The significance level

Answer 9

The probability of a Type I error

A significance level must be specified to select the critical values for the test.

Question 10

• The power of a test

Answer 10

• The probability of rejecting the null when it is false.
• The power of a test = 1 − P(Type II error)

Question 11

• The p-value

Answer 11

the smallest significance level for which the hypothesis would be rejected.

Question 12

Degree of freedom

Answer 12

T - statistic (1 and 2 population): n-1
Chi - square (1 population): n-1
F - statistic (2 population): n1-1, n2-1

Question 13

• Parametric tests

Answer 13

like the T-test, F-test, and Chi-square test, make assumptions regarding the distribution of the population from which samples are drawn.

Question 14

• Nonparametric tests

Answer 14

• Either do not consider a particular population parameter or have few assumptions about the sampled population.
• Nonparametric tests are used when the assumptions of parametric tests can’t be supported, or when the data are not suitable for parametric tests.

Question 15

To test a hypothesis that a population correlation coefficient equals zero

Answer 15

This test statistic follows a t-distribution with n − 2 degrees of freedom
- T = r*căn (n-2)/căn (1 – r^2)
o R: sample correlation
o Degree of freedom = n-2

Question 16

Spearman rank correlation test

Answer 16

a nonparametric test,
- can be performed when we have only ranks (e.g.,
deciles of investment performance)
- can be used to test
whether two sets of ranks are correlated

Question 17

Spearman rank correlation test with sample size > 30

Answer 17

When the sample size is greater than 30, the test statistic follows a t-distribution
with n − 2 degrees of freedom.

Question 18

Contingency table data

Answer 18

A contingency or two-way table shows the number of observations from a sample that have a combination of two characteristics.

Question 19

Tests of independence based on contingency table data

Answer 19

• Using Chi-square statistic:
  + X^2 = Sum (O - E)/E
  + E= (total row i x total column j)/sum (total row + column)
• The degrees of freedom are (r − 1) × (c − 1)
• If the test statistic is greater than the
  critical chi-square value for a given level of significance, we reject the hypothesis
  that the two characteristics are independent.