Hypothesis testing

Question 1

Stuff to talk about here:

• Null hypothesis
• Alternative hypothesis
• Finding critical value and critical region
• Maybe there’s more?

Answer 1

Ye perhaps there’s more

Question 2

What is a hypothesis?

Answer 2

An assumption or claim about a certain value of a population parameter. Most of the time they be using p, just like them binomial stuff.

Question 3

What is the null hypothesis?
How do u write one?

Answer 3

It’s symbol is H₀ and it’s like the “currently accepted value” of a certain “hypothesis”

To write one:
E.g. Checking to see if a coin was biased in favour of heads.
The null hypothesis would be that it wasn’t biased.
∴ p = 0.5

probability of it being heads is 0.5

Question 4

What is the alternative hypothesis?
How do u write one?

Answer 4

It’s symbol is H1 (teeny one) and it’s the “researched hypothesis” and is involved in claims that need to be tested

To write one:
E.g. Still checking if coin biased in favour of heads.
The alternative hypothesis would be that it is biased.
∴ p > 0.5

probability of it being heads is greater than 0.5

Question 5

How do u even write a test statistic?

Answer 5

I mean u just state a way to check if it’s biased or not so…. yeah.

Or not, i actually dunno how

Question 6

How to find critical value if p < 0.4?

X~B(10.0.4) significance level 0.05 (they always tell u the significance level)

H₀: p = 0.4 H1: p < 0.4

Answer 6

Example:

X~B(10.0.4) significance level 0.05 (they always tell u the significance level)

H₀: p = 0.4 H1: p < 0.4

1) p< therefore find first probability that exceeds 0.05 which is given as significance level.
2) U do binomial CD
3) P(X≤2) = 0.1673
4) Critical value is 1 less than this so u write:
Critical value is X = 1
Critical region is X ≤ 1

Therefore H₀ is rejected as it don’t equal 0.4?

Question 7

How to find critical value if p > 0.4?

X~B(10.0.4) significance level 0.05 (they always tell u the significance level)

H₀: p = 0.4 H1: p > 0.4

Answer 7

Example:

X~B(10.0.4) significance level 0.05 (they always tell u the significance level)

H₀: p = 0.4 H1: p > 0.4

1) p> therefore find first probability that exceeds 1 - 0.05 = 0.95 (significance level still)
2) Also still binomial CD
3) P(X≤7) = 0.9877
4) Critical value is 1 more than this so u write:
Critical value is X = 8
Critical region is X ≥ 8

So for any random sample taken, H₀ rejected if X ≥ 8 as it’s in the critical region and so you can conclude that p > 0.4

Question 8

How to find critical value if p ≠ 0.4?

X~B(10.0.4) significance level 0.05 (they always tell u the significance level)

H₀: p = 0.4 H1: p ≠ 0.4

Answer 8

Example:

X~B(10.0.4) significance level 0.05 (they always tell u the significance level)

H₀: p = 0.4 H1: p ≠ 0.4

1) It’s gonna be a 2 tailed test ∴ u must divide significance level by 2:
0.05 / 2 = 0.025
2) p≠ therefore find first probability that exceeds 0.025 and
exceeds 1 - 0.025 = 0.975
(so basically the whole package with that new significance level)

3) Always will be binomial CD
4) P(X≤1) = 0.0464 (exceeds 0.025)
P(X≤7) = 0.9877 (exceeds 0.975)

5) Critical values are x = 0 and x = 8
Critical regions are X ≤ 0 and X ≥ 8

So for another random sample taken, H₀ can be rejected if X ≥ 8 or X ≤ 0 concluding that p ≠ 0.4

Question 9

What about doing p-values edition?

Answer 9

So for this one, only use this if not given significance level:

1) Same as the rest tbh but u just use significance level of 0.5 and apparently the answer has gotta be: 0.01 < n < 0.05
2) Do all ur stuff
3) Figure out of there’s enough evidence to reject H₀

I should probably add an actual question yano…