An organization claims that the number of prospective home buyers who want their next house to be larger, smaller or the same size as their current house is not uniformly distributed. To test this claim, you randomly select 800 prospective home buyers and ask them what size they want their next house to be. The table given below shows the results. At α = 0.05, test the organization’s claim.

Response        Frequency, f

Larger ……...………    285

Same size ………..     224

Smaller ……..……..     291

(a) Identify the expected distribution and state H₀ and H_a,

(b) Find the critical value and identify the rejection region,

(c) Find the chi-square test statistic,

(d) Decide whether to reject or fail to reject the null hypothesis,

(e) Interpret the decision in the context of the original claim.