Simple Hypothesis Test (Bit rusty)

[tb9069]

Hi, im a third year mathematician and have just started a new unit called theory of inference, and am having trouble with a question. I know it's an easy question really, however I am slightly rusty at these sorts of things and need a little help:

I read the following recently:

We observed 100 normal weight diners and 100 obese diners at chinese buets
in California, Minnesota, and New York, and noted whether they were eating
with chopsticks or [forks]. Out of 33 people with chopsticks, 26 were normal-
weighted and only 7 were obese.
You are to test the null hypothesis that the probability of a normal-weight person eating
with chopsticks is the same as the probability of an obese person eating with chopsticks.

You will need to go through the following stages.
1. Organise your data into a table.
2. Choose a statistical model for X, the number of normal-weight people eating with
chopsticks, and Y , the number of obese people eating with chopsticks.
3. Based on your statistical model, specify the null hypothesis that you want to test,
and the direction in which you want to reject.
4. Choose a test statistic which will be large in the direction that you want to reject.
5. Determine the distribution of this test statistic under the null hypothesis (sometimes
referred to as the `null distribution'). Hint: you will want to make a Normal
approximation to the Binomial distribution at this stage.
6. Evaluate the P-value of your observations. You should be able to do most of the
approximate calculation on the back of an envelope (you will also need statistical
tables, or R, at the nal stage).
7. Now compute an exact P-value: this will involve a simple simulation in R.

Help would be much appreciated thankyou