Final answer:
a) For small sample sizes and unknown population standard deviation, use a t-test. b) Use a chi-square test to compare data sets from unknown distributions. c) Assume a normal distribution when sample is random and population is approximately normal. d) Non-parametric tests can be used when data assumptions are not met.
Step-by-step explanation:
a) A t-test is suitable when the sample size is small and the population standard deviation is unknown. The sample standard deviation is utilized to estimate the population standard deviation, and the t-distribution is employed in place of the normal distribution.
b) When the distribution is unknown, a chi-square test can be used to determine if two data sets are from the same distribution. In this test, values are compared between observed and predicted, assuming same distributions.
c) When the population is roughly normally distributed and the data originates from a simple, random sample, or when the sample size is large and the population standard deviation is known, it is appropriate to assume a normal distribution.
d) Non-parametric tests can be used when the data does not meet the assumptions of parametric tests. These tests do not rely on specific distribution assumptions, but they may have less power compared to parametric tests.