Week 7 - Fundamentals of Hypothesis Testing

Question 1

What is a hypothesis?

Answer 1

A claim about a population parameter (mean, proportion etc.)

Question 2

What is Type I Error?

Answer 2

The one where we reject a true null hypothesis, it is considered a serious type of error. Probability of this error is alfa, level of significance.

Question 3

What is a Type II Error?

Answer 3

Where we fail to reject a false null hypothesis. The probability of this error is beta.

Question 4

What is the power of a test?

Answer 4

The probability of rejecting a null hypothesis that is false.

It increases as the sample size increases.

Question 5

What is the p-value?

Answer 5

Probability of obtaining a test statistic more extreme ( ≤ or >= ) than the observed sample value given H0 is true.

also called observed level of significance

Question 6

Is this an upper-tail test or a lower-tail test?
H0 : μ ≤ 3
H1: μ > 3

Answer 6

This is an upper-tail test since the
alternative hypothesis is focused on
the upper tail above the mean of 3.

Question 7

Is this an upper-tail test or a lower-tail test?
H0: μ ≥ 3
H1: μ < 3

Answer 7

This is a lower-tail test since the
alternative hypothesis is focused on
the lower tail below the mean of 3

Question 8

What hypothesis test is this?
H0: μ = 3
H1: μ =/ 3

Answer 8

two-tail test

Question 9

What is the difference in hypothesis tests where σ is known and where it isn’t?

Answer 9

If it is known, then we convert the sample result to a z value, if it isn’t then we convert the sample result to a t test statistic.