Q. 10 - The Practice of Statistics for AP

Question

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. Since not all questionnaires in a survey of this type are returned, researchers decided to investigate the relationship between the response rate and the size of the business. The data are given in the following two-ways

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

Step-by-Step Solution

Answer

The data is supported by Option B.

Step 1: Given Information

Given: The data are given in the following two-ways :

It can conclude from the preceding statistics that option (b), small businesses appear to have a higher response rate than medium or large businesses, is correct.

Step 2: Explanation for correct option

The rate of percentage of small companies is $\left(\frac{125}{200}\right)=6.25\%$

The rate of percentage of Medium companies is $\left(\frac{81}{200}\right)= 40.5\%$

The rate of percentage of Large companies is $\left(\frac{40}{200}\right)= 20\%$

According to the above data of three sizes, small businesses have a higher response rate than the other two.

As a result, option B is in favor of the data.

Step 3: Explanation for incorrect option

(a) There are more small companies than large companies in the survey, does not supported by the data.

(c) Exactly the same number of companies responded as didn’t respond, does not supported by the data.  

(d) Small companies dislike larger companies, does not supported by the data. 

(e) If we combined the medium and large companies, then their response rate would be equal to that of the small company,does not supported by the data.