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Chapter 7: Problem 22

To determine if patrons are satisfied with performance quality, a theater surveys patrons at an evening performance by placing a paper survey inside their programs. All patrons receive a program as they enter the theater. Completed surveys are placed in boxes at the theater exits. On the evening of the survey, 500 patrons saw the performance. One hundred surveys were completed, and \(70 \%\) of these surveys indicated dissatisfaction with the performance. Should the theater conclude that patrons were dissatisfied with performance quality? Explain.

Short Answer

Expert verified
No, the theatre shouldn't conclude that the majority of the patrons were dissatisfied. Based on the data given, only 14% of all patrons indicated dissatisfaction. However, since not all patrons completed the survey, this data might not accurately represent the views of all patrons.

Step by step solution

01

Understand the provided data

On the given night, there were 500 patrons, out of which 100 completed the survey. Out of these 100, 70% were dissatisfied.
02

Calculate the actual number of dissatisfied patrons who completed the survey

70 percent of the respondents from the total of 100 were dissatisfied, it's calculated as: \(0.70 * 100 = 70\) patrons.
03

Determine the dissatisfaction rate among all patrons

Now calculate the dissatisfaction rate among all patrons, not just those who filled out the survey. This is done by dividing the number of dissatisfied patrons who completed surveys (70) by the total number of patrons (500). So, it's \(70/500 = 0.14\) or \(14%\)
04

Draw conclusions

An initial conclusion might state that 70% of patrons were dissatisfied with the performance based solely on completed survey data. However, in accurate terms, considering all the patrons who watched the performance that night, only 14% have shown dissatisfaction. This representation may or may not be say the overall satisfaction of the entire audience, considering that not everyone filled out the survey.

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