Question

A department store, A, has four competitors: B,C,D, and E. Store A hires a consultant to determine if the percentage of shoppers who prefer each of the five stores is the same. A survey of 1100 randomly selected shoppers is conducted, and the results

about which one of the stores shoppers prefer are below. Is there enough evidence using a

significance level α = 0.05 to conclude that the proportions are really the same?

1. Store A B C D E
2. Number of Shoppers 262 234 204 190 210

Answer 1

Answer:-

Given That:-

A department store, A, has four competitors: B,C,D, and E. Store A hires a consultant to determine if the percentage of shoppers who prefer each of the five stores is the same. A survey of 1100 randomly selected shoppers is conducted, and the results about which one of the stores shoppers prefer are below. Is there enough evidence using a significance level α = 0.05 to conclude that the proportions are really the same?

Given,

(i) The null hypothesis :

The population frequencies are equal to the expected frequencies (to be calculated below).

(ii) The alternative hypothesis :

The null hypothesis is false.

(iii)  

(iv) The degrees of freedom:

k - 1 = 5 -1

= 4

(v) The test statistic can be calculated using a table:

Peference	% of Shoppers	E	O	O - E
A	20%	0.2 * 1100 = 220	262	42	1764	8.018
B	20%	0.2 * 1100 = 220	234	14	196	0.891
C	20%	0.2 * 1100 = 220	204	-16	256	1.163
D	20%	0.2 * 1100 = 220	190	-30	900	4.091
E	20%	0.2 * 1100 = 220	210	-10	100	0.455

= 14.618

(vi) From and k - 1 = 4

The critical value is 9.488.

(vii) Is there enough evidence to reject ?

Since , there is enough statistical evidence to reject to reject the null hypothesis and to believe that customers do not prefer each of the five stores equally.

Thank you for your supporting. Please upvote my answer...