Question

2 part question
PART 1.
A political candidate has asked you to conduct a poll to determine what percentage of people support her.

If the candidate only wants a 10% margin of error at a 90% confidence level, what size of sample is needed?

Give your answer in whole people.

PART 2.

You intend to conduct a goodness-of-fit test for a multinomial distribution with 3 categories. You collect data from 77 subjects.

What are the degrees of freedom for the χ2 distribution for this test?
d.f. =

Answer 1

Anwer 1

it is clear that no prior estimate of proportion is given, so we will use the following formula for determination of sample size n

where z = 1.645 (using z distribution table) and margin of error ME = 10% or 10/100 = 0.10

setting the values, we get

rounding it to nearest whole number, we get

Required sample size n = 68

Answer 2

We know that to show 3 categories for 77 subjects, so we have k = 3 (number of categories, not number of observations)

Formula for degree of freedom for  goodness-of-fit test for a multinomial distribution is given as

df = k-1

where k=3

so, it gives us

df = 3-1 = 2

Therefore, degree of freedom is 2