Reading 11: Hypothesis Testing

Question 1

Test Statistic Formula

Hypothesis Testing

11.1

Answer 1

Question 2

Standard Error

(When we know the population standard deviation)

Hypothesis Testing

11.2

Answer 2

Question 3

Standard Error

(Sample standard deviation)

Hypothesis Testing

11.3

Answer 3

Question 4

Test Statistic for Hypothesis Tests of the Population Mean

(Practical Case - Population Variance Unkown)

Hypothesis Testing

11.4

Answer 4

If the population sampled has unkown variance and either of the conditions below holds:

• The sample is large, or
• The sample is small but the population sampled is normally distributed, or approximately normally distributed

then the test statistic for hypothesis tests concerning a single population mean is below.

Where:

t_n-1 = t-stat with n-1 degrees of freedom (n is sample size)

x bar = sample mean

u₀ = the hypothesized value of the population mean

s = the sample standard deviation

Question 5

Z-Test Alternative

(population sampled is normally distributed with known variance)

Hypothesis Testing

11.5

Answer 5

Question 6

Z-Test Alternative

(unknown variance; large sample)

Hypothesis Testing

11.6

Answer 6

Question 7

Test Statistic for a Test of the Difference between Two Population Means

(Normally Distributed Populations, Population Variances Unknown but
Assumed Equal)

Hypothesis Testing

11.7

Answer 7

Question 8

Test Statistic for a Test of the Difference between Two Population Means

(Normally Distributed Populations, Unequal and Unknown Population Variances)

Hypothesis Testing

11.8

Answer 8

Question 9

Modified Degrees of Freedom

Hypothesis Testing

11.9

Answer 9

Question 10

Sample Mean Difference

Hypothesis Testing

11.10

Answer 10

n is the number of pairs of observations

Question 11

Sample Variance

(of sample mean difference)

Hypothesis Testing

11.11

Answer 11

Question 12

Standard Error of the Mean Difference

Hypothesis Testing

11.12

Answer 12

After taking the square root of the sample variance:

Question 13

Test Statistic for a Tests Concerning the Value of a Population Variance

(Normal Population; Chi Square)

Hypothesis Testing

11.14

Answer 13

If we have n independent observations from a normally distributed population, the appropriate test statistic is:

Question 14

Sample Variance

Hypothesis Testing

11.15

Answer 14

Question 15

Test Statistic for Tests Concerning Differences between the Variances of Two Populations

(F-Test; normally distributed populations)

Hypothesis Testing

11.16

Answer 15

Question 16

Spearman Rank Correlation

Hypothesis Testing

11.17

Answer 16

Question 17

Large Sample T-test

(solving for t)

Hypothesis Testing

11.18

Answer 17

Question 18

Test Statistic for a Test of Mean Differences

(Normally Distributed Populations, Unknown Population Variances)

Hypothesis Testing

11.13

Answer 18