Quantitative Methods - Hypothesis Testing - Hypothesis Tests and Types of Errors

Question 1

define a hypothesis

Answer 1

a statement about a population’s parameter

Question 2

what are the 7 steps in hypothesis testing?

Answer 2

1) state the hypothesis
2) select a test statistic
3) specify the level of significance (probability in the tails)
4) state the decision rule for the hypothesis
5) collect the sample and calculate statistics
6) make a decision about the hypothesis
7) make a decision based on the test results

Question 3

what is the null hypothesis?

Answer 3

• the hypothesis to be tested
• what the researcher wants to reject
• always includes the equal sign
• contains equals sign, greater or equal to sign or less than or equal to sign

Question 4

that is the alternative hypothesis?

Answer 4

• what the researcher would like to conclude

- what is concluded if the researcher rejects the null hypothesis

Question 5

what are the two outcomes an alternative hypothesis can be?

Answer 5

one or two sided

Question 6

what is the difference betwene a one and two sided test?

Answer 6

one-tailed: if your alternative hypothesis is either greater than or less than your null hypothesis

two-tailed: allow for deviation on sides of the hypothesised value (0). whenever the alternative hypothesis doesn’t equal the null hypothesis

Question 7

what are the two components that make up a test statistic

Answer 7

• calculated from sample data

- compared to critic value(s) to test the null hypothesis

Question 8

what are critic values similar to?

Answer 8

confidence intervals

Question 9

what is a type I error? What is the probability of the error?

Answer 9

the rejection of a null hypothesis when it is actually true e.g. value falling into tail

• the significance level

Question 10

what is a type II error? what is the probability of the error?

Answer 10

the failure to reject a null hypothesis when it is false

• the power of a test is 1 - the probability of a type II error

Question 11

what is the decision for a hypothesis test?

Answer 11

reject the null hypothesis or fail to reject the null hypothesis (aka the decision rule)

Question 12

explain a decision rule and relationship between confidence intervals and hypothesis tests

Answer 12

we set up confidence intervals around our sample/point estimate and see whether the value falls in these to reject/accept the null

e.g. if a hypothesized mean falls outside the confidence interval for the population mean, we reject the hypothesis that the population mean = hypothesised mean

Question 13

what are possible reasons for statistical significance not necessarily implying economic significance

Answer 13

• transaction costs
• taxes
• risk