Modules Week 3

Question 1

What is null hypothesis significance testing?

Answer 1

• Propose a null hypothesis that a population parameter (mean) has a particular value.
• Proceed assuming the null hypothesis is true.
• Determine the probability of the sample mean occurring if the null hypothesis is true.
• If the probability of the sample mean occurring is small, reject the null hypothesis. If the probability is large, do not reject the null hypothesis.

Question 2

What is the Alpha level/level of significance?

Answer 2

5% + We’ve said that we would reject the null hypothesis if the probability of observing our sample means was small.

Question 3

What is the 5% Alpha level?

Answer 3

The alpha level defines which sample means in a distribution of sample means are expected or typical, and which are unlikely or extreme, if the null hypothesis is true.

Question 4

When the comparison distribution is __________ _______, the critical limits set by the ____ Alpha Level are precisely________ standard errors from the mean of the distribution.

Answer 4

perfectly normal, 5%, +/-1.96

Question 5

If our sample mean is________ ______ _______, the probability is _____than 5%, and therefore, _____.

______reject the null hypothesis

Answer 5

inside these limits, greater, high, do not

Question 6

If our sample mean is _____ _____ ______, the probability is ___ than 5%, and therefore, ____.

______ the null hypothesis

Answer 6

outside these limits, lower, low, reject

Question 7

What is a single-sample z-test?

Answer 7

Now that an Alpha Level of 5% has been set, we must determine the probability of our sample mean occurring.

We can do this by performing a single sample z-test. In other words, we will calculate a z-score for our sample mean.

In this context, a z-score will express how many standard errors our sample mean is away from H₀.

Question 8

What is the formula for a z-test?

Answer 8

z = M - μ/ σₘ
M= sample mean
μ = population mean
σₘ = standard error of the mean

Question 9

Run through the example on Notion (Groot 6) and ensure all is understood

Answer 9

Notion

Question 10

Is population standard deviation often known?

Answer 10

No
In instances when we don’t know the population standard deviation, we can’t use a z-test and the normal distribution to assess our sample mean. That’s okay! Instead, we can use a t-test and the ‘t-distribution’.

We use sample standard deviation as an estimate of population standard deviation. Single sample t-tests and z-tests are very similar otherwise

Question 11

Are almost all aspects of t vs z testing the same?

Answer 11

Yes, Almost all aspects of the process are the same when conducting either a single sample t-test or z-test.

We still use Null Hypothesis Significance Testing.

We still assign a value that indicates no effect to the null hypothesis, and proceed assuming the null is true.

We still apply an alpha level of 5% and determine the probability of our mean occurring. The result determines whether the null hypothesis is rejected or not.

Question 12

What is one difference about a T- distribution?

Answer 12

In the t-distribution, the critical limit corresponding to our alpha level of 5% will not be fixed at +/- 1.96 as it was with the z-test and normal distribution.

Instead, the t-distribution requires that we consider sample size and degrees of freedom (df), when determining the probability of the sample mean. Degrees of Freedom are one less than our sample size for a single sample t-test (n - 1).

The critical limit varies along with df.

Question 13

Discuss the example on notion (Groot 7)

Answer 13

Notion

Question 14

Discuss textbook example in notion (groot 7)

Answer 14

Notion