3. Inferential Statistics

Question 1

What is the central limit theorem?

Answer 1

The sampling distribution of the sample mean approximates the normal distribution, regardless of the distribution of the population mean from which the samples are drawn if the sample size is sufficiently large

Question 2

How can the central limit theorem be used?

Answer 2

It can be used to make statistical inferences based on the properties of the normal distribution even if the sample is drawn from a population that is not normally distributed

Question 3

What is a “sufficiently large” sample size with regards to the central limit theorem?

Answer 3

n=10-15 if the population distribution is close to normal, n=40+ if the distribution is heavily skewed

Question 4

What are the steps for hypothesis testing?

Answer 4

1. Develop a research hypothesis that can be tested mathematically
2. Formally state the null and alternative hypotheses
3. Decide on a test, gather the data, do the calculations
4. Make your decision based on the results

Question 5

What is the difference between a single-tailed and two-tailed alternative hypothesis?

Answer 5

For the null hypothesis to be rejected with a single-tailed alternative hypothesis, the result mean must either be greater than or less than the expected mean (one or the other depending on the hypothesis); with a two-tailed alternative hypothesis, the result mean must not be equal to the expected mean

Question 6

What is a Type-I error?

Answer 6

The null hypothesis is true but rejected

Question 7

What is a Type-II error?

Answer 7

The null hypothesis is false but is not rejected

Question 8

What is power?

Answer 8

1 - Beta (beta = probability of Type-II error)