statistical inference and hypothesis testing

Question 1

Inference in statistics

Answer 1

• In statistics, we can distinguish between descriptive and inferential statistics.
• Descriptive statistics describes or summarizes the data.
• Inferential statistical aims to draw general conclusions from empirical data.

Question 2

An example problem of statistical inference

Answer 2

• Let’s consider the following situation: A box contains 100 coins. Some of these coins are gold, and the rest are silver. If we sample n = 25 coins with replacement and get m = 7 gold coins, what does this tell us about the true number of gold coins in the box?
• Ultimately, in this problem, we are interested in knowing the true proportion of gold coins in the box of 100. We denote this proportion by g (g for gold).
• We can use a so-called hypothesis test to try to infer this value

Question 3

hypothesis testing

Answer 3

• The hypothesis test allows us to assess whether any given value for g is compatible with the number of gold coins that we got in our sample.
• For example, a hypothesis test could be applied to the hypothesis that the true value of g is 0.5, i.e. there are 50 gold and 50 silver coins in the box of 100.
• Doing so, we effectively ask, If the true number of gold coins in the box of is 50, then is getting 7 gold coins in a sample of 25 something that we should expect or not?

Question 4

Sampling distributions

Answer 4

• To test a hypothesis we must first determine what would be expected if the hypothesis was true.
• For example, if our hypothesis is that the value of g is 0.5 (i.e. 50 gold coins in the box), how many gold coins should we expect if we sampled n = 25 coins from this box?
• More specifically, we calculate the probability of obtaining each possible number of gold coins in the sample (i.e. each number from 0 to 25) under this assumption.
• These probabilities are given by what is known as the sampling distribution.