A marketing research firm conducted a survey of companies in its state. They mai

Question

A marketing research firm conducted a survey of companies in its state. They mailed a questionnaire to 300 small companies, 300 medium-sized companies, and 300 large companies. The rate of nonresponse is important in deciding how reliable survey results are. Here are the data on response to this survey.

(a) What was the overall percent of nonresponse? (Round your answer to one decimal place.)
  %

(b) Describe how nonresponse is related to the size of the business. (Use percents to make your statements precise. Round your answers to one decimal place.)

(c) Draw a bar graph to compare the nonresponse percents for the three size categories. (Do this on paper. Your instructor may ask you to turn in this work.)

(d) Using the total number of responses as a base, compute the percent of responses that come from each of small, medium, and large businesses.

(e) The sampling plan was designed to obtain equal numbers of responses from small, medium, and large companies. In preparing an analysis of the survey results, do you think it would be reasonable to proceed as if the responses represented companies of each size equally?

Yes, the response percentages are very similar for all three sizes of business.

No, the response percentages differ between the three sizes of business.    

No, the response percentages are very similar for all three sizes of business.

Yes, the response percentages differ between the three sizes of business.

Response Size of company Yes No Total Small 170 130 300 Medium 141 159 300 Large 124 176 300

Explanation / Answer

(a) Overall percentage of Non response = (130+159+176)/900 = 51.67%

(b)

Small = (130/300) * 100 = 43.33%, Medium = (159/300) * 100 = 53%, Large = (176/300) * 100 = 58.67%

(c)

(d)

  Small = (170/300) * 100 =56.67%, Medium = (141/300) * 100 = 47%, Large = (124/300) * 100 = 41.33%

(e) No, the response percentages differ between the three sizes of business.  

% Non Response Small 43.33% Medium 53.00% Large 58.67%

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