Question

According to an article in marketing news, fewer checks are being written at grocery store checkout stands than in the past. to determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below. check written year 1 year 2 year 3 yes 225 175 125 no 275 325 375 referring to table above, the expected number of shoppers who pay by check in year 1 if there is no difference in the proportion of shoppers who pay by check among the three years is

Answer 1

Given:
check written        year 1         year 2        year 3
yes                         225            175             125
no                          275            325              375 


The expected number of shoppers who pay by check in year 1 if there is no difference in the proportion of shoppers who pay by check among the three years is 175.

Each year has 500 customers, and its proportion of customers paying in check gradually decreased from 45% to 25%. If there is no difference in proportion, I am assuming that the data is averaged. Thus, (225+175+125) / 3 = 525 / 3 = 175.