/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 22 To determine if patrons are sati... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The Perry Preschool Project was created in the early 1960 s by David Weikart in Ypsilanti, Michigan. In this project, 123 African American children were randomly assigned to one of two groups: One group enrolled in the Perry Preschool, and one group did not enroll. Follow-up studies were done for decades. One research question was whether attendance at preschool had an effect on high school graduation. The table shows whether the students graduated from regular high school or not and includes girls only (Schweinhart et al. 2005). $$\begin{array}{lcc}\hline & \text { Preschool } & \text { No Preschool } \\\\\hline \text { HS Grad } & 21 & 8 \\ \text { No HS Grad } & 4 & 17\end{array}$$ a. Find the percentages that graduated for both groups, and compare them descriptively. Does this suggest that preschool was associated with a higher graduation rate? b. Which of the conditions fail so that we cannot use a confidence interval for the difference between proportions?

In 2018 it was estimated that approximately \(45 \%\) of the American population watches the Super Bowl yearly. Suppose a sample of 120 Americans is randomly selected. After verifying the conditions for the Central Limit Theorem are met, find the probability that at the majority (more than \(50 \%\) ) watched the Super Bowl. (Source: vox.com)

A recent Monmouth University poll found that 675 out of 1008 randomly selected people in the United States felt that college and universities with big sports programs placed too much emphasis on athletics over academics. Assuming the conditions for using the CLT were met, use the Minitab output provided to answer these questions. $$\begin{aligned}&\text { Descriptive Statistics }\\\&\begin{array}{rrrr}\mathrm{N} & \text { Event } & \text { Sample p } & 95 \% \mathrm{Cl} \text { for } \mathrm{p} \\\\\hline 1008 & 675 & 0.669643 & (0.639648,0.698643)\end{array}\end{aligned}$$ a. Complete this sentence: I am \(95 \%\) confident that the population proportion believing that colleges and universities with big sports programs place too much emphasis on athletics over academics is between _____ and _______. Report each number as a percentage rounded to one decimal place. b. Suppose a sports blogger wrote an article claiming that the majority of Americans believe that colleges and university with big sports programs place too much emphasis on athletics over academics. Does this confidence interval support the blogger's claim? Explain your reasoning.

From Formula \(7.2\), an estimate for margin of error for a \(95 \%\) confidence interval is \(m=2 \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\) where \(\mathrm{n}\) is the required sample size and \(\hat{p}\) is the sample proportion. Since we do not know a value for \(\hat{p}\), we use a conservative estimate of \(0.50\) for \(\hat{p}\). Replace \(\hat{p}\) with \(0.50\) in the formula and simplify.

According to a 2018 Rasmussen Poll, \(40 \%\) of American adults were very likely to watch some of the Winter Olympic coverage on television. The survey polled 1000 American adults and had a margin of error of plus or minus 3 percentage points with a \(95 \%\) level of confidence. a. State the survey results in confidence interval form and interpret the interval. b. If the Rasmussen Poll was to conduct 100 such surveys of 1000 American adults, how many of them would result in confidence intervals that included the true population proportion? c. Suppose a student wrote this interpretation of the confidence interval: "We are \(95 \%\) confident that the sample proportion is between \(37 \%\) and \(43 \%\)." What, if anything, is incorrect in this interpretation?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.