# S2 Two tailed Hypothesis Test

Watch
Announcements

Page 1 of 1

Go to first unread

Skip to page:

I am a bit confused on how to perform two tailed tests. For example on question 7 on the jan 2006 paper, for part (a) they test P(X>9) and part (b) P(x<18), why don't they do P(X<9) or P(X>18)?? Basically how do you know which tail to test when you have two?

I understand hypothesis testing I don't understand how to perform a test with two tails to pick from, please can someone help me as the exam is soon and i'm panicking

(I have uploaded pics of the question and mark scheme)

Thank you!

I understand hypothesis testing I don't understand how to perform a test with two tails to pick from, please can someone help me as the exam is soon and i'm panicking

(I have uploaded pics of the question and mark scheme)

Thank you!

0

reply

Report

#2

(Original post by

I am a bit confused on how to perform two tailed tests. For example on question 7 on the jan 2006 paper, for part (a) they test P(X>9) and part (b) P(x<18), why don't they do P(X<9) or P(X>18)?? Basically how do you know which tail to test when you have two?

I understand hypothesis testing I don't understand how to perform a test with two tails to pick from, please can someone help me as the exam is soon and i'm panicking

(I have uploaded pics of the question and mark scheme)

Thank you!

**Katiee224**)I am a bit confused on how to perform two tailed tests. For example on question 7 on the jan 2006 paper, for part (a) they test P(X>9) and part (b) P(x<18), why don't they do P(X<9) or P(X>18)?? Basically how do you know which tail to test when you have two?

I understand hypothesis testing I don't understand how to perform a test with two tails to pick from, please can someone help me as the exam is soon and i'm panicking

(I have uploaded pics of the question and mark scheme)

Thank you!

Try it with n=25 and you'll see that x=9 is one of the sufficiently unlikely outcomes on the high side. You can try it with n=100 too although the question asks for an approximation of course.

1

reply

Report

#3

**Katiee224**)

I am a bit confused on how to perform two tailed tests. For example on question 7 on the jan 2006 paper, for part (a) they test P(X>9) and part (b) P(x<18), why don't they do P(X<9) or P(X>18)?? Basically how do you know which tail to test when you have two?

I understand hypothesis testing I don't understand how to perform a test with two tails to pick from, please can someone help me as the exam is soon and i'm panicking

(I have uploaded pics of the question and mark scheme)

Thank you!

Same thing applied for part (b), only in this case the number of students is lower than the expected number (i.e 20 students are expected to read the Deano from these samples in total) thus they test P(X<18). Hope this makes sense

3

reply

(Original post by

In part (a), if the percentage of pupils that read the Deano was in fact 20%, then you would expect to find 4 students from the sample who read the Deano. However, in the sample there are 9 students who read the book, which exceeds the expected number (i.e 4 students). Hence they test P(X>9), or in other words, they test how 'far' the data exceed the expectation. If it is too far from what we expect (probability is less than 5% sig. level in this case) then the hypothesis 20% is statistically incorrect

Same thing applied for part (b), only in this case the number of students is lower than the expected number (i.e 20 students are expected to read the Deano from these samples in total) thus they test P(X<18). Hope this makes sense

**NDVA**)In part (a), if the percentage of pupils that read the Deano was in fact 20%, then you would expect to find 4 students from the sample who read the Deano. However, in the sample there are 9 students who read the book, which exceeds the expected number (i.e 4 students). Hence they test P(X>9), or in other words, they test how 'far' the data exceed the expectation. If it is too far from what we expect (probability is less than 5% sig. level in this case) then the hypothesis 20% is statistically incorrect

Same thing applied for part (b), only in this case the number of students is lower than the expected number (i.e 20 students are expected to read the Deano from these samples in total) thus they test P(X<18). Hope this makes sense

And I solve it like a one tailed test?

0

reply

Report

#5

(Original post by

Ohh ok, I think I see where I was getting confused. So for part (a) my hypotheses are null hyp: p=0.2, alt hyp: p>0.2 .... and for part (b) my hypotheses would be null hyp: p=0.2, alt hyp p<0.2 ??

And I solve it like a one tailed test?

**Katiee224**)Ohh ok, I think I see where I was getting confused. So for part (a) my hypotheses are null hyp: p=0.2, alt hyp: p>0.2 .... and for part (b) my hypotheses would be null hyp: p=0.2, alt hyp p<0.2 ??

And I solve it like a one tailed test?

and they are both two-tailed tests

EDIT: Give me 5 mins, I will type out a detailed solution for this question so that you can understand it better.

0

reply

Report

#6

**Katiee224**)

Ohh ok, I think I see where I was getting confused. So for part (a) my hypotheses are null hyp: p=0.2, alt hyp: p>0.2 .... and for part (b) my hypotheses would be null hyp: p=0.2, alt hyp p<0.2 ??

And I solve it like a one tailed test?

The question has the phrase "...is different from 0.2."

If you use a one tailed test instead then, roughly speaking, your critical region will be too big.

0

reply

(Original post by

No, for both parts it would be:

and they are both two-tailed tests

EDIT: Give me 5 mins, I will type out a detailed solution for this question so that you can understand it better.

**NDVA**)No, for both parts it would be:

and they are both two-tailed tests

EDIT: Give me 5 mins, I will type out a detailed solution for this question so that you can understand it better.

(Original post by

No. In both cases the alternative hypothesis is .

The question has the phrase "...is different from 0.2."

If you use a one tailed test instead then, roughly speaking, your critical region will be too big.

**BuryMathsTutor**)No. In both cases the alternative hypothesis is .

The question has the phrase "...is different from 0.2."

If you use a one tailed test instead then, roughly speaking, your critical region will be too big.

So I could essentially solve it like a one-tailed test once I have halfed the significance level?

1

reply

Report

#9

(Original post by

Oh ok, I understand what you guys mean with the hypotheses

**Katiee224**)Oh ok, I understand what you guys mean with the hypotheses

**So I could essentially solve it like a one-tailed test once I have halfed the significance level?**
0

reply

Thank you for the help both of you, if I get an A on monday it will be down to your help

1

reply

Report

#11

**Katiee224**)

I am a bit confused on how to perform two tailed tests. For example on question 7 on the jan 2006 paper, for part (a) they test P(X>9) and part (b) P(x<18), why don't they do P(X<9) or P(X>18)?? Basically how do you know which tail to test when you have two?

I understand hypothesis testing I don't understand how to perform a test with two tails to pick from, please can someone help me as the exam is soon and i'm panicking

(I have uploaded pics of the question and mark scheme)

Thank you!

__Part (a)__

at 5% sig. level

Expected number of pupils who read the Deano .

Observed number is thus we need to

1/ calculate the probability that the number of pupils who read Deano is 9 or greater under

2/ check if this probability is smaller than 2.5% or not (as this is a two-tailed test). If it is smaller than 2.5%, then we reject our null hypothesis.

*(we are looking at the upper tail here)*

Perform the test

This means the probability of is too small for to be true at this level of significance. Hence we reject our null hypothesis, there is evidence at 5% significant level that the percentage of pupils that read Deano is not 20%.

__Part (b)__

at 5% sig. level

Expected number of pupils who read the Deano .

Observed number is thus we need to

1/ calculate the probability that the number of pupils who read Deano is 18 or smaller under

2/ check if this probability is smaller than 2.5% or not (as this is a two-tailed test). If it is smaller than 2.5%, then we reject our null hypothesis.

*(we are looking at the other tail here)*

Use normal approximation to make the calculation easier -> perform the test -> Conclusion as in the mark scheme.

Hope this helps

0

reply

X

Page 1 of 1

Go to first unread

Skip to page:

### Quick Reply

Back

to top

to top