What are the seven steps to the hypothesis testing procedure?
- State the hypothesis
- Select the appropriate test statistic
- Specify the level of significance
- State the decision rule regarding the hypothesis
- Collect the sample and calculate sample statistics
- Make a decision regarding the hypothesis
- Make a decision based on the results of the test
What is the null hypothesis?
The null hypothesis is what the researcher wants to reject.
What is the alternative hypothesis?
The alternative hypothesis is what the researcher wants to prove, and it is accepted when the null hypothesis is rejected.
Describe the difference between a two sided alternative hypothesis and a one-sided alternative hypothesis:
- A two-tailed test results from a two-sided alternative hypothesis (e.g., Ha: μ ≠ μ0).
- A one-tailed test results from a one-sided alternative hypothesis (e.g., Ha: μ > μ0, or Ha: μ < μ0).
What is a test statistic?
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:
What is a type I error?
The rejection of the null hypothesis when it is actually true.
The failure to reject the null hypothesis when it is actually false.
What is the significance level?
- 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).
- A significance level must be specified to select the critical values for the test.
What is a decision rule?
When hypothesis testing compares a computed test statistic to a critical value at a stated level of significance (the decision rule for the test).
What is the power of a test?
The probability of rejecting the null when it is false. The power of a test = 1 − P(Type II error).
Explain the relation between confidence intervals and hypothesis tests:
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.
Does a statistically significance imply economic significance?
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.
What is the p-value for a hypothesis test?
- The p-value for a hypothesis test is the smallest significance level for which the hypothesis would be rejected.
- Ex: a p-value of 7% means the hypothesis can be rejected at the 10% significance level but cannot be rejected at 5%.
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?
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?
What statistic can be used to test two means from two independent normally distributed populations?
For two independent samples from two normally distributed populations, the difference in means can be tested with a t-statistic.
What is the denominator based on when two population variances are assumed to be equal?
The denominator is based on the variance of the pooled samples.
What is the denominator based on when two population variances are assumed to be unequal?
The denominator is based on a combination of the two samples’ variances.
What a paired comparisons test concerned with?
The mean of the differences between the paired observations of two dependent, normally distributed samples.
What statistic is used to test whether the means of two dependent normal variables are equal?
- A t-statistic
- Values outside the critical t-values lead us to reject equality.
What is a chi-square test used for?
To test a hypothesis about the population variance for a normally distributed population.
What is the test comparing two variances based on independent samples from two normally distributed populations?
F-distributed test statistic.
What are parametric tests?
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.
What are nonparametric tests?
- Either do not consider a particular population parameter or have few assumptions about the sampled population.
- Used when the assumptions of parametric tests can’t be supported or when the data are not suitable for parametric tests.
