What is the Significance of Testing Population Variance in a Sample?

[gxc9800]

Homework Statement

Given that 8 person vote for Mr Tan , i can't understand why the probability is sum of 0 people vote for him until 8 people vote for him. Why not the probability = 22c8 ( (0.6)^8 )( (0.4)^14) ?

Homework Equations

The Attempt at a Solution

 

[RUber]

Why not the probability = 22c8 ( (0.6)^8 )( (0.4)^14) ?

The probability $22c8 ( (0.6)^8 )( (0.4)^14)$ is the likelihood of drawing exactly this sample assuming the claim is true. When testing the hypothesis, you are comparing the cumulative probability of this sample (at least 8 people), against the claim.
Note that the expected value, assuming his claim is true would be $22(.6)=13.2$ people. If you just take the probability of 13 people saying they support him, that will not be 50%, but the cumulative probability will be close to that.

 

[gxc9800]

hi, When testing the hypothesis, you are comparing the cumulative probability of this sample (at least 8 people), against the claim

why the author doesn't say 'the investigator selects a random smaple of 22 people and at most 8 people agree to vote for him ' instead?

 

[RUber]

The question is: How likely is it to find something at least as extreme as what was observed? That is normally what people mean when they talk about p-values and significance. It is not: What is the probability of pulling this sample assuming that H0 is true?
The author may not state it, but that is what is always meant by testing significance.