Chi-squared Tests

Question 1

Explain why these data could possibly be modelled by a discrete uniform distribution.

Answer 1

Each box has an equal chance of being opened- each box is expected to be opened (20) times.

Question 2

Why is there always one constraint?

Answer 2

Expected frquencies must add up to 100

Question 3

How many constraints are there for binomial & poisson respectively?

Answer 3

1 (+ 1 if porbability/ mean is not given)

Question 4

Rev. Ex. 2 Q5b
The head of English suggested that the Director was losing accuracy by combining thr English grades C to U in one row. He suggested that the Director should split the English grades into two rows, grades C or D and grades E or U as for Maths.

State why this might lead to problems in performing the test.

Answer 4

• increasing the number of data cells–> some may have expected frequencies less than 5
• will require merging some rows and/or columns to perform the chi-squared test

Question 5

Formula for estimating p for geometric

Answer 5

1/ E(x)

Question 6

Explain why the degree of freedom is 3 when the sample size is 4. (1)

Answer 6

only constraint is that the totals agree