Question

Directions: Solve the following problems, detailing and documenting the solutions. Additional instructions: For each problem, be sure to include the (a) type of parametric or nonparametric testing being performed; (b) both null and research hypotheses; (c) critical value and test statistic; (d) p-value; and (e) both technical and contextual conclusions. 1. The back offices for the five department stores that anchor Pinelands Promenade Mall dispute whether or not they receive comparable treatment by mall management. In response, mall management hired a consulting firm to investigate whether or not customer preferences among shoppers for these five department stores are comparable or equivalent. Research assistants collected a random sample of 240 people at the mall, asking these mall visitors which department store they preferred most. The resulting frequency data was as follows: Onyx Paisley’s Quarterdeck Regal Sale-Mart 54 60 36 48 42 What should the consulting firm report to mall management? In other words, according to the available evidence, and testing at the 5% level of significance, is the proportion of mall visitors who prefer each of the five department stores at Pinelands Promenade the same? [COMMENTS & HINTS: It is good to see how the data fits the claim.]

Answer 1

This test is non-parametric test, as we don't know the population parameters

Following set pf hypothesis we want to test,

• H₀: The proportion of visitors preferred store is the same in each store: p₁ = p₂ = p₃ = p₄ =p₅
• H_a: The proportion of cases is not the same in each store: at least one p_i is different from the others

From this,

(c) critical value and test statistic;

Chi-Square Test Statistic = 9.375

Critical Value = 9.4877 - From chi square table

(d) p-value;

p-value = 0.05238

(e) both technical and contextual conclusions.

As p-value is greater than 0.05 we fail to reject the null hypothesis.

Hence, H₀: The proportion of visitors preferred store is the same in each store: p₁ = p₂ = p₃ = p₄ =p_{5 is true.}

_{Conclusion - Visitors preferred all the stores in the same proportions.}