(R11) Hypothesis Testing

Question 1

Null Hypothesis

Answer 1

The hypothesis that the researcher wants to reject, denoted Ho; The hypothesis that is actually tested and is the basis for the selection of the test statistics.

Question 2

Alternative hypothesis

Answer 2

The hypothesis that we want to validate

Question 3

Steps in hypothesis testing

Answer 3

1. State the hypothesis
2. Identify the appropriate test statistic (t or z) and its probability distribution
3. Specify level of confidence
4. State the decision rule
5. Collect data and calculate the test statistic
6. Make the decision
7. Make the real world decision

Question 4

Two-tailed test for the population mean

Answer 4

Ho: u = uo,
Ha: u =/ uo

Question 5

One-tailed test for the population mean

Answer 5

Ho: u <= uo
Ha: u > uo

Question 6

Test-Statistic Calculation

Answer 6

(Sample Statistic - Hypothesized Value) / SE of sample

Question 7

2 Types of Errors in Hypothesis Testing

Answer 7

Type 1: The rejection of null hypothesis when it is actually true (alpha = probability of type 1 error)
Type 2: The failure to reject the null hypothesis when it is actually false

Question 8

Power of a test in hypothesis testing

Answer 8

Probability of correctly rejecting the null (rejecting the null when it is false)

= 1 - probability of type two error

Question 9

When doing hypothesis testing, what must be compared to the test statistic?

Answer 9

Compare to the critical value (use alpha to look up critical value in tables).

For one tailed tests, if the test statistic is greater than the critical value, you reject the null

Question 10

P-Value

Answer 10

Smallest level of significance at which null hypothesis can be rejected; the smaller the p-value the stronger the evidence (if you have p-value of .0342, you can reject null hypothesis at an alpha of .05 but not .01)

Question 11

For two tailed tests with an alpha of 10%, how much percentage would be in each tail?

Answer 11

Divide alpha by two since its a two tailed test (5% in each tail)

Question 12

Hypothesis for testing the differences between means

Answer 12

Ho: u1 - u2 = 0
Ha: u1 - u2 =/ 0

You can also change the equal signs to greater than or less then

Question 13

Pooled variances

Answer 13

Used with t-statistics for testing the means of two normally distributed populations are equal, when the variances of the population are unknown but assumed to be equal.

Question 14

Chi-square Test

Answer 14

Test used for hypothesis testing concerning the variance of a normally distributed population.

Question 15

Chi-Square Calculation

Answer 15

ChiSquare = (n-1)s^2 / sigma^2

s= sample variance
sigma^2 = hypothesized population variance

Question 16

F-Test

Answer 16

Test concerned with the equality of the variances of two populations, used when the populations are normally distributed.

Question 17

F-Test Calculation

Answer 17

F = s1^2 / s2^2

s1^2 = Variance of s1
s2^2 = Variance of s2

Question 18

Parametric Tests

Answer 18

Tests that rely on assumptions regarding the distribution of the population and are specific to population parameters

Question 19

Nonparametric tests

Answer 19

Tests that do no consider a particular population parameter or have few assumptions about the population that is sampled.