Hypothesis Testing

Question 1

What are the seven steps to the hypothesis testing procedure?

Answer 1

1. State the hypothesis
2. Select the appropriate test statistic
3. Specify the level of significance
4. State the decision rule regarding the hypothesis
5. Collect the sample and calculate sample statistics
6. Make a decision regarding the hypothesis
7. Make a decision based on the results of the test

Question 2

What is the null hypothesis?

Answer 2

The null hypothesis is what the researcher wants to reject.

Question 3

What is the alternative hypothesis?

Answer 3

The alternative hypothesis is what the researcher wants to prove, and it is accepted when the null hypothesis is rejected.

Question 4

Describe the difference between a two sided alternative hypothesis and a one-sided alternative hypothesis:

Answer 4

1. A two-tailed test results from a two-sided alternative hypothesis (e.g., Ha: μ ≠ μ0).
2. A one-tailed test results from a one-sided alternative hypothesis (e.g., Ha: μ > μ0, or Ha: μ < μ0).

Question 5

What is a test statistic?

Answer 5

The test statistic is the value that a decision about a hypothesis will be based on. For a test about the value of the mean of a distribution:

Question 6

What is a type I error?

Answer 6

The rejection of the null hypothesis when it is actually true.

Answer 7

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

Question 8

What is the significance level?

Answer 8

1. Can be interpreted as the probability that a test statistic will reject the null hypothesis by chance when it is actually true (i.e., the probability of a Type I error).
2. A significance level must be specified to select the critical values for the test.

Question 9

What is a decision rule?

Answer 9

When hypothesis testing compares a computed test statistic to a critical value at a stated level of significance (the decision rule for the test).

Question 10

What is 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

Explain the relation between confidence intervals and hypothesis tests:

Answer 11

A hypothesis about a population parameter is rejected when the sample statistic lies outside a confidence interval around the hypothesized value for the chosen level of significance.

Question 12

Does a statistically significance imply economic significance?

Answer 12

Statistical significance does not necessarily imply economic significance. Even though a test statistic is significant statistically, the size of the gains to a strategy to exploit a statistically significant result may be absolutely small or simply not great enough to outweigh transactions costs.

Question 13

What is the p-value for a hypothesis test?

Answer 13

1. The p-value for a hypothesis test is the smallest significance level for which the hypothesis would be rejected.
2. Ex: a p-value of 7% means the hypothesis can be rejected at the 10% significance level but cannot be rejected at 5%.

Question 14

What is the appropriate test statistic for a population mean of both large and small samples when the population is normally distributed and the variance is known?

Answer 14

Question 15

What is the appropriate test statistic for a population mean of both large and small samples when the population is normally distributed and the variance is unknown?

Answer 15

Question 16

What statistic can be used to test two means from two independent normally distributed populations?

Answer 16

For two independent samples from two normally distributed populations, the difference in means can be tested with a t-statistic.

Question 17

What is the denominator based on when two population variances are assumed to be equal?

Answer 17

The denominator is based on the variance of the pooled samples.

Question 18

What is the denominator based on when two population variances are assumed to be unequal?

Answer 18

The denominator is based on a combination of the two samples’ variances.

Question 19

What a paired comparisons test concerned with?

Answer 19

The mean of the differences between the paired observations of two dependent, normally distributed samples.

Question 20

What statistic is used to test whether the means of two dependent normal variables are equal?

Answer 20

• A t-statistic
• Values outside the critical t-values lead us to reject equality.

Question 21

What is a chi-square test used for?

Answer 21

To test a hypothesis about the population variance for a normally distributed population.

Question 22

What is the test comparing two variances based on independent samples from two normally distributed populations?

Answer 22

F-distributed test statistic.

Question 23

What are parametric tests?

Answer 23

Parametric tests, like the t-test, F-test, and chi-square tests, make assumptions regarding the distribution of the population from which samples are drawn.

Question 24

What are nonparametric tests?

Answer 24

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