/*! 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} Q 24. Brushing teeth, wasting water? A... [FREE SOLUTION] | 91影视

91影视

Brushing teeth, wasting water? A recent study reported that fewer than half of young adults turn off the water while brushing their teeth. Is the same true for teenagers? To find out, a group of statistics students asked an SRS of 60 students at their school if they usually brush with the water off. How many

students in the sample would need to say 鈥淣o鈥 to provide convincing evidence that fewer than half of the students at the school brush with the water off? The Fathom dot plot below shows the results of taking 200 SRSs of 60 students from a population in which the true proportion who brush with the

water off is 0.50.

(a) Suppose 27 students in the class鈥檚 sample say 鈥淣o.鈥 Explain why this result does not give convincing evidence that fewer than half of the school鈥檚 students brush their teeth with the water off.

(b) Suppose 18 students in the class鈥檚 sample say 鈥淣o.鈥 Explain why this result gives strong evidence that fewer than 50% of the school鈥檚 students brush

their teeth with the water off.

Short Answer

Expert verified

Part (a) It is not sufficient evidence to that more than half of the school鈥檚 student brush their teeth with the water off .

Part (b) It is sufficient evidence to that more than half of the school鈥檚 student brush their teeth with the water off .

Step by step solution

01

Part (a) Step 1. Given Information    

The dot plot depicts the result of taking 200 SRSs from 60 kids from a population with a real proportion of 0.50 brushing with the water off.

02

Part (a) Step 2. Concept Used 

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between 0 (never happens) and 1 (happens frequently) (always occurs).

03

Part (a) Step 3. Explanation     

Because 27 out of 60 kids answered "No," it does not provide persuasive proof that more than half of the school's students recycle 27/60=0.45 We can see that the proportion of 0.45 has a lot of dots above it in the dot plot. Thus, a proportion of 0.45 is quite likely to be obtained when the true proportion is 0.5, and there is insufficient evidence to support the assertion that more than half of the school's students wash their teeth with the water turned off.

04

Part (b) Step 1. Explanation  

Because 18 out of 60 kids answered "Yes," this statistic strongly suggests that the majority of the school's students recycle 18/60=0.3We can see that the proportion of 0.5 has no dot above it and no dots to the left of it in the supplied dot plot. Thus, when the genuine proportion is 55, it is extremely likely to achieve a proportion of 0.3, and there is adequate evidence to support the assertion that more than half of the school's students brush their teeth with the water turned off.

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

Color-blind men About7%of men in the United States have some form of red-green color blindness. Suppose we randomly select one U.S. adult male at a time until we find one who is red-green color-blind. How many men would we expect to choose, on average? Design and carry out a simulation to answer this question. Follow the four-step process.

A Titanic disaster Refer to Exercise 64.

(a) Find P(survived | second class).

(b) Find P(survived).

(c) Use your answers to (a) and (b) to determine whether the events 鈥渟urvived鈥 and 鈥渟econd class鈥 are independent. Explain your reasoning.

Mac or PC? A recent census at a major university revealed that40% of its students primarily used Macintosh computers (Macs). The rest mainly used

PCs. At the time of the census, 67% of the school鈥檚 students were undergraduates. The rest were graduate students. In the census, 23% of respondents were graduate students who said that they used PCs as their

main computers. Suppose we select a student at random from among those who were part of the census.

(a) Assuming that there were 10,000 students in the census, make a two-way table for this chance process.

(b) Construct a Venn diagram to represent this setting.

(c) Consider the event that the randomly selected student is a graduate student who uses a Mac. Write this event in symbolic form using the two events of interest that you chose in (b).

(d) Find the probability of the event described in (c). Explain your method.

Find P(L). Interpret this probability in context.

Going pro Only 5%of male high school basketball, baseball, and football players go on to play at the college level. Of these, only1.7% enter major league professional sports. About 40% of the athletes who compete in college and then reach the pros have a career of more than3 years.16 What is the probability that a high school athlete who plays basketball, baseball, or football competes in college and then goes on to have a pro career of more than 3 years? Show your work.

See all solutions

Recommended explanations on Math Textbooks

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.