Hey I am doing some final exam revision and I came across this question on chi-squared testing. (the sample data information has also been given but I have to sort the information myself).

I'd just like some guidance and maybe steps as to how I could approach this q and whether it is a goodness of fit or independence test. I think it is a goodness of fit test but I'm a bit unsure. The sample size is 293 by the way.

Belle also recently heard in the media that the proportion of sales are as follows:

35% of sales are apartments;

45% of sales are houses;

10% of sales are townhouses;

5% of sales are villas and;

5% of sales are other.

Belle would like to know if the sample data is statistically different to what the media is suggesting. Remember to state your assumptions and limitations of the result.

There is also a marking criteria to help us see if we are on the right track and it says:

1.Chi Squared test - Hypothesis testing- There are four parts to this:

a.Correctly define the null and alternate hypothesis

b.Decision rule or P-value approach

c.Test statistic calculation

d.Draw the appropriate calculation in the context of the claim.

2.Chi Squared Test - Assumptions

a.Invoke CLT for large n.

b.Define "alpha" or use P-value and discuss the conventional value of "alpha"

c.Others

3.Chi Squared Test - Limitations

a.Sample subject to errors.

b.Outliers that may skew your results (remember you are using the mean).

c.Other

I am a bit confused because I didn't know that you could invoke the central limit theorem for a chi-squared test. If we do invoke CLT how does it change the results?

Regardless, I'd just like a little bit of guidance as to how I should approach this question