Q T1.10. - 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-way table: 

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 companies.

Step-by-Step Solution

Answer

The correct option is (b).

Step 1: Given Information

The table is 

Size	Response	No response	Total
Small	125	75	200
Medium	81	119	200
Large	40	160	200

Step 2: Concept

Statistical Measures are a descriptive-analytical technique that provides an overview of a data set's properties.

Step 3: Calculation

We 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. 

The following is how the response rates for the three business sizes are calculated: Small: $$\begin{gathered} percent= \frac{125}{200}\times 100 \\ =0.625\times 100 \\ =6.25\% \end{gathered}$$

Medium: $$\begin{gathered} percent= \frac{81}{200} \times 100 \\ =0.405\times 100 \\ =40.5\% \end{gathered}$$

Large: $$\begin{gathered} percent= \frac{40}{200}\times 100 \\ =0.2\times 100 \\ =20\% \end{gathered}$$

According to the above data of three sizes, small businesses have a higher response rate than the other two. Option (b) is correct.