Chapter 20: Testing Hypotheses About Proportions

Question 1

Define ‘Null hypothesis’.

Answer 1

The claim being assessed in a hypothesis test. Usually, the null hypothesis is a statement of “no change from the traditional value”, “no effect”, “no difference”, or “no relationship”. For a claim to be a testable null hypothesis, it must specify a value for some population parameter that can form the basis for assuming a sampling distribution for a test statistic.

Question 2

Define ‘Alternative hypothesis’.

Answer 2

Proposes what we should conclude if we find the null hypothesis to not be plausible.

Question 3

Define ‘P-value’.

Answer 3

The probability of observing a value for a test statistic at least as far from the hypothesized parameter as the statistic value actually observed if the null hypothesis is true. A small P-value indicates either that the observation is improbable or that the probability calculation was based on incorrect assumptions. The assumed truth of the null hypothesis is the assumption under suspicion.

Question 4

Define ‘One-proportion z-test’.

Answer 4

A test of the null hypothesis that the proportion parameter for a single population equals a specified value (H0: p=p0) by referring the statistic z= (p̂ - p0) / SD (p̂ ) to a standard Normal model.

Question 5

Define ‘Effect size’.

Answer 5

The difference between the null hypothesis value and the true value of a model parameter.

Question 6

Define ‘Two-sided alternative (Non-directional alternative)’.

Answer 6

An alternative hypothesis is two-sided (HA: p ≠ p0) when we are interested in deviations in either direction away from the null hypothesis value and the true value of a model parameter value.

Question 7

Define ‘One-sided alternative (Directional alternative)’.

Answer 7

An alternative hypothesis is one-sided (HA: p > p0 or HA: p < p0) when we are interested in deviations in only one direction away from the hypothesized parameter value.

Question 8

How do you perform a hypothesis test for a proportion?

Answer 8

1. The null hypothesis has the form H0: p = p0
2. Find the SD of the sampling distribution of the sample proportion by assuming that the null hypothesis is true: SD (p̂ ) = sqrt( p0 q0 /n)
3. Refer the statistic z= (p̂ - p0) / SD (p̂ ) to a standard Normal model.

Question 9

What does a small P-value mean? A large one?

Answer 9

• Small P-value indicates that the statistic we have observed would be unlikely were the null hypothesis true. Leads us to doubt the null.
• Large P-value tells us that there is insufficient evidence to doubt the null. However, does not prove the null true.

Question 10

What is the difference between a confidence interval and hypothesis test?

Answer 10

• A hypothesis test assesses the plausibility of the value of a parameter value, by determining the degree to which the sample provides contradictory evidence (the P-value).
• A confidence interval shows the range of plausible values for the parameter.