126k views
5 votes
A survey was designed to study how business operations vary according to their size. companies were classified as small, medium, or large. questionnaires were sent to 200 randomly selected businesses of each size. because not all questionnaires were returned, researchers decided to investigate the relationship between the response rate and the size of the business. the data are given in the two-way table.

size response no response total
small 125 75 200
medium 81 119 200
large 40 160 200
Which of the following conclusions seems to be supported by the data?

(a) There are more small companies than large companies in the survey.

(b) Small companies appear to have a higher response rate than medium or big companies.

(c) Exactly the same number of companies responded as didn’t respond.

(d) Small companies dislike larger companies.

(e) If we combined the medium and large companies, then their response rate would be equal to that of the small company

User Dan Simon
by
8.5k points

1 Answer

3 votes

In the given data, option (b) seems to be supported. Small companies had the highest response rate (125/200), suggesting they are more likely to respond compared to medium and large companies. Option (a) is not supported by the data, as the table does not provide information about the total number of companies. Options (c) and (d) are not accurate interpretations of the data. Option (e) is not directly supported by the data, as the response rates for medium and large companies are different.

The data suggests that small companies exhibit a higher response rate than their medium and large counterparts. The response rates are 62.5% for small companies, 40.5% for medium companies, and 20% for large companies. This discrepancy in response rates implies that smaller businesses are more likely to participate in the survey compared to medium and large businesses. However, it's important to note that the size of the companies in the survey is not indicative of their prevalence in the overall business landscape, as the data only provides information on the response rates within the surveyed sample.

Option (a) is not supported because the table doesn't provide information on the total number of small, medium, or large companies in the survey. Options (c) and (d) are not accurate conclusions to draw from the data. The data does not indicate an equal number of responses and non-responses, and it does not suggest any preference or dislike between small and large companies. Option (e) is not directly supported because the response rates for medium and large companies are different, but it does highlight the potential for comparing response rates between combined medium and large companies and small companies in future analysis.

User Peter Moberg
by
8.5k points