1. What is the difference between a parametric and a non-parametric test? Give an example of each type of test and explain when they are appropriate to use. Answer: A parametric test is a statistical test that assumes that the data follow a certain distribution, such as the normal distribution, and that the parameters of the distribution, such as the mean and the standard deviation, are known or can be estimated from the sample. A non-parametric test is a statistical test that does not make any assumptions about the distribution of the data and only uses the ranks or signs of the observations. An example of a parametric test is the t-test, which compares the means of two groups and assumes that the data are normally distributed and have equal variances. An example of a non-parametric test is the Mann-Whitney U test, which compares the medians of two groups and does not assume any distribution or equality of variances. Parametric tests are appropriate to use when the data meet the assumptions of normality, homogeneity of variance, and independence of observations. Non-parametric tests are appropriate to use when the data do not meet these assumptions or when the data are ordinal or nominal. Rationale: This question tests the students' understanding of the basic concepts and definitions of parametric and non-parametric tests, as well as their ability to apply them to different situations. 2. What is a confidence interval and how is it related to a hypothesis test? How do you interpret a 95% confidence interval for a population mean? Answer: A confidence interval is a range of values that contains the true population parameter with a certain level of confidence, based on the sample data. A hypothesis test is a procedure that uses the sample data to test a claim about the population parameter, such as whether it is equal to, greater than, or less than a certain value. A confidence interval and a hypothesis test are related because they both use the same sample statistic and standard error to calculate their results. However, a confidence interval provides an estimate of the population parameter with a margin of error, while a hypothesis test provides a decision to reject or fail to reject the null hypothesis with a level of significance. To interpret a 95% confidence interval for a population mean, we can say that we are 95% confident that the true population mean lies within the interval, or that if we repeated the sampling process many times, 95% of the intervals would contain the true population mean. Rationale: This question tests the students' understanding of the concept and interpretation of confidence intervals, as well as their relationship to hypothesis tests. 3. What is a p-value and how is it used in hypothesis testing? What does it mean if the p-value is less than 0.05? Answer: A p-value is the probability of obtaining a sample statistic as extreme or more extreme than the observed one, assuming that the null hypothesis is true. It is used in hypothesis testing to measure how compatible the sample data are with the null hypothesis. The smaller the p-value, the less compatible the data are with the null hypothesis, and the more evidence there is against it. If the p-value is less than 0.05, it means that there is less than 5% chance of obtaining such an extreme result by chance alone, if the null hypothesis is true. Therefore, we can reject