You are Here: Home >< Maths

# S2 - Hypothesis Testing watch

1. Ok this is the question:

It is suggested that one-third of all mathematicians are left-handed. In a survey, 51 out of 174 mathematicians were found to be left-handed. Assuming that the sample was random, carry out a test, at the 5% significance level, of whether or not the sample confirms the suggestion.

I know it is a binomial distribution, so:

Now here comes my question, how do I know it is , rather than .

I know how to do the rest, just this bit. Help is very much appreciated. Thanks in advance!

- Italy v Holland now
2. i don't think it's any massive reason, just that common sense says those figures make less than a third
surely if you did it the other way round and took it away from 1 you'd get the same answer anyway?
3. (Original post by T89)
Ok this is the question:

It is suggested that one-third of all mathematicians are left-handed. In a survey, 51 out of 174 mathematicians were found to be left-handed. Assuming that the sample was random, carry out a test, at the 5% significance level, of whether or not the sample confirms the suggestion.

I know it is a binomial distribution, so:

Now here comes my question, how do I know it is , rather than .

I know how to do the rest, just this bit. Help is very much appreciated. Thanks in advance!

- Italy v Holland now
Your hypothesis is correct and so we have a 2 tail test. The expected value is 58 and the observed value is 51. Hence you want to see is this observed value is in the lower tail - it can't be in the upper tail! Hence you work out the probability that x is <= 51.
{If your observed value had been 63, for example, then you would work out the probability that x >= 63.}
4. Oh yeah ok makes sense now! Thanks a lot!
5. If you wanted you could have just found the critical regions first, although it is slightly more work, most questions of that type will ask you to do that as a first stage and then later say, x number were left handed what does this mean.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: June 9, 2008
Today on TSR

### Oxford Interviews

Find out which colleges are sending invitations

### University open days

• University of East Anglia
Fri, 23 Nov '18
• Norwich University of the Arts
Fri, 23 Nov '18
• Edge Hill University
Sat, 24 Nov '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams