Q T1.9. - 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.

What percent of all small companies receiving questionnaires responded? $\left(a\right) 12.5\% \left(c\right) 33.3\% \left(e\right) 62.5\% \left(b\right) 20.8\%$

Step-by-Step Solution

Answer

The correct option is (e) $62.5\%$

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 have $125$people based on the information provided.

According to the information provided, $125$ small businesses responded to the $200$ questions. As a result, the following formula is used to calculate the  $$\begin{gathered} Percent=\frac{125}{200} \times 100 \\ = 0.625\times 100 \\ = 62.5\% \end{gathered}$$

Therefore, $62.5\%$ of small companies receiving questionnaires responded.

The correct option is (b).