We saw in 20.1 that there are 3 different possible Alternate Hypotheses we can choose from:
The true value is greater than the null value
\[H_A: \mu > \mu_0\]
The true value is less than the null value
\[H_A: \mu < \mu_0\]
The true value is different from the null value
\[H_A: \mu \ne \mu_0\]
(Discuss the three test types and their relationship to the level of significance)
The Critical Region
Using the Test Statistic and the Critical Region
Example
Let’s revisit and solve the example brought up in 20.1:
American mental abilities are often measured by an IQ test. The IQ distribution is normal with a mean of 100 and a population standard deviation of 15. A random sample of 40 Snow College students is taken and they have an average IQ of 106.3. Can we say with a 5% level of significance that the true average IQ of Snow College students is higher than the nation?
To solve, let’s do the following:
Make sure the Central Limit Theorem (CLT) holds
Define our hypotheses
Find the critical region
Find the test statistic
Practice
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After solving on your own, check the solution:
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After solving on your own, see solution here
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After solving on your own, see solution here
## Problem 20.3.1
A popover is an element that is placed on top of everything else.
* Item 1
* Item 2
$$\bar{x}=\frac{1}{n}\sum x$$
It can be used when you want to tell something important.
## Problem 20.3.2
A popover is an element that is placed on top of everything else.
* Item 1
* Item 2
$$\bar{x}=\frac{1}{n}\sum x$$
It can be used when you want to tell something important.
## Problem 20.3.3
A popover is an element that is placed on top of everything else.
* Item 1
* Item 2
$$\bar{x}=\frac{1}{n}\sum x$$
It can be used when you want to tell something important.