Question: In a study of the responsiveness of small businesses in different locations, questionnaires were sent to 200 randomly chosen small businesses in rural and small-town locations, 200 randomly chosen small businesses in suburban areas, and 200 randomly chosen small businesses in urban areas. The numbers of businesses of each type that responded to the questionnaire were recorded. Here is a table of the results.

Rural or small-town Suburban Urban

Responded 115 96 79

Did not respond 85 104 121

We wish to know whether the data provide sufficient evidence to conclude that the distributions of response rates for small businesses in these three locations are not all the same. Show the hypotheses. Show the conditions are satisfied and the steps. Show the calculations for the chi square test statistic. Indicate the degrees of freedom. Sketch the chi-square distribution to show the P-value. Conclude in context.