Question

all the workers in a company were asked a survey question. the two - way frequency table shows the responses from the workers in the day shift and night shift. complete parts a and b.

1. is there evidence of an association between the response and the shift? explain. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

oa. yes. in the day shift, % of workers in the day shift answered \yes.\ however, in the night shift, only % answered \yes.\
ob. no. the relative frequencies are all very close in value.

Explanation:

Step1: Calculate the percentage of "Yes" responses in the day shift

The formula for percentage is \(\frac{\text{Number of "Yes" responses in day shift}}{\text{Total number of day - shift workers}}\times100\).
For the day shift, the number of "Yes" responses is \(59\) and the total number of day - shift workers is \(100\). So the percentage is \(\frac{59}{100}\times100 = 59\%\).

Step2: Calculate the percentage of "Yes" responses in the night shift

The formula for percentage is \(\frac{\text{Number of "Yes" responses in night shift}}{\text{Total number of night - shift workers}}\times100\).
For the night shift, the number of "Yes" responses is \(21\) and the total number of night - shift workers is \(100\). So the percentage is \(\frac{21}{100}\times100=21\%\).

Answer:

A. Yes. In the day shift, \(59\%\) of workers in the day shift answered "Yes." However, in the night shift, only \(21\%\) answered "Yes."