1. What is the difference between a population and a sample? How do you calculate the sample mean and the sample standard deviation? A population is the entire group of individuals or objects that we want to study, while a sample is a subset of the population that we actually collect data from. The sample mean is the average of the sample values, calculated by adding up all the sample values and dividing by the sample size. The sample standard deviation is a measure of how much the sample values vary from the sample mean, calculated by taking the square root of the average of the squared deviations from the sample mean. 2. What is a confidence interval and how do you interpret it? How do you construct a 95% confidence interval for the population mean when the population standard deviation is known? A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. To interpret a confidence interval, we say that we are confident that the population parameter is between the lower and upper bounds of the interval. To construct a 95% confidence interval for the population mean when the population standard deviation is known, we use the formula: sample mean ± 1.96 * (population standard deviation / square root of sample size). 3. What is a hypothesis test and what are the steps involved in conducting one? What are the null and alternative hypotheses, and how do you choose between them? A hypothesis test is a statistical procedure that allows us to make a decision about a population parameter based on sample data. The steps involved in conducting a hypothesis test are: 1) state the null and alternative hypotheses, 2) choose a significance level, 3) calculate the test statistic and the p-value, 4) compare the p-value to the significance level and draw a conclusion. The null hypothesis is the statement that we assume to be true unless there is strong evidence against it, while the alternative hypothesis is the statement that we want to test and that contradicts the null hypothesis. We choose between them based on the p-value: if the p-value is less than or equal to the significance level, we reject the null hypothesis and accept the alternative hypothesis; if the p-value is greater than the significance level, we fail to reject the null hypothesis and do not accept the alternative hypothesis.