Notebook + Quiz: Simulating from the Null

Simulating From the Null Hypothesis

In the previous lesson on confidence intervals, we saw how we could simulate a sampling distribution for a statistic by bootstrapping our sample data. Alternatively, in hypothesis testing, we could simulate a sampling distribution from the null hypothesis using characteristics that would be true if our data were to have come from the null.

In this notebook, you will walk through this process, and answer some quiz questions to solidify your understanding.

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QUIZ QUESTION: :

Quiz 1 : Use the first question above to match the null and alternative to the appropriate statements.

ANSWER CHOICES:

Null or Alternative	Statement
The average height for the sample of coffee drinkers is not the same as the average height for the sample for non-coffee drinkers.
The average height for all coffee drinkers is not the same as the average height for all non-coffee drinkers.
The average height for the sample of coffee drinkers is the same as the average height for the sample for non-coffee drinkers.
The average height for all coffee drinkers is the same as the average height for all non-coffee drinkers.

SOLUTION:

Null or Alternative	Statement
The average height for all coffee drinkers is not the same as the average height for all non-coffee drinkers.
The average height for all coffee drinkers is the same as the average height for all non-coffee drinkers.

QUIZ QUESTION: :

Quiz 2 : Use the second question above to match the null and alternative to the appropriate statements.

ANSWER CHOICES:

Null or Alternative	Statement
The average height for all coffee drinkers is the same or less than the average height for all non-coffee drinkers.
The average height for all coffee drinkers is the same or greater than the average height for all non-coffee drinkers.
The average height for all coffee drinkers is greater than the average height for all non-coffee drinkers.
The average height for all coffee drinkers is less than the average height for all non-coffee drinkers.

SOLUTION:

Null or Alternative	Statement
The average height for all coffee drinkers is the same or greater than the average height for all non-coffee drinkers.
The average height for all coffee drinkers is less than the average height for all non-coffee drinkers.

QUIZ QUESTION: :

Quiz 3 : Use the results of your sampling distributions for question 3 above to match the following values to the correct description.

ANSWER CHOICES:

Description	Value
Normal
0.24
The Law of Large Numbers
0.41
Skewed
The Central Limit Theorem
0.47

SOLUTION:

Description	Value
Normal
0.24
0.41
The Central Limit Theorem
0.47

Use your solutions about the sampling distribution, and what difference in means would be likely from the null hypothesis to mark all of the below that are true.

We can expect the standard deviation of the sampling distribution for differences from the null to be essentially the same as what we observed from the data.

If the null hypothesis is true, we would expect the difference in means of coffee drinkers and non-drinkers to be zero.

The observed sample mean difference between coffee drinkers and non-coffee drinkers in sample_data appears as though it came from the sampling distribution you simulated for the null hypothesis.

SOLUTION:

We can expect the standard deviation of the sampling distribution for differences from the null to be essentially the same as what we observed from the data.
If the null hypothesis is true, we would expect the difference in means of coffee drinkers and non-drinkers to be zero.