/*! 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 40. Walking to school Refer to Exerc... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Q 40. (page 581)

Walking to school Refer to Exercise 36.

a. Explain why the sample result gives some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.

c. What conclusion would you make?

Short Answer

Expert verified

a. Sample proportion of 0.17<0.13.

b. Z=1.19,P=0.1170

c. No enough convincing evidence is present that true population proportion of all students at elementary school who walk is>0.13

Step by step solution

01

Given Information

It is given that 伪=0.05

H0:p=0.13

H1:p>0.13

n=100,x=17

02

Explaining Sample Results

The sample proportion is:

p^=xn=17100=0.17

As 0.17>0.13, sample result gives some evidence for alternate hypothesis as it agrees with it.

Hence,H1:p>0.17

03

Standardized test statistic and P value

As sample proportion is 0.17

Test statistic is z=p^-p0p01-p0n=0.17-0.130.13(1-0.13)100=1.19

Pvalue is P=P(z>1.19)=1-P(Z<1.19)=1-0.8830

P=0.1170

04

Conclusion

We get

P=P(z>1.19)=1-P(Z<1.19)=1-0.8830=0.1170

Now, P>0.05鈬�Fail to rejectH0

Hence, there is no enough convincing evidence that true population of all students>0.13

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

Roulette An American roulette wheel has 18red slots among its 38slots. To test if a particular roulette wheel is fair, you spin the wheel 50times and the ball lands in a red slot 31times. The resulting P-value is0.0384.

a. Interpret the P-value.

b. What conclusion would you make at the伪=0.05 level?

c. The casino manager uses your data to produce a99% confidence interval for p and gets(0.44,0.80). He says that this interval provides convincing evidence that the wheel is fair. How do you respond

18%Members of the city council want to know if a majority of city residents supports a 1%increase in the sales tax to fund road repairs. To investigate, they survey a random sample of 300city residents and use the results to test the following hypotheses:

H0:p=0.50

Ha:p>0.50

where pis the proportion of all city residents who support a 1%increase in the sales tax to fund road repairs.

In the sample, p^=158/300=0.527, The resulting P-value is 0.18. What is the correct interpretation of this P-value?

a. Only 18% of the city residents support the tax increase.

b. There is an 18%chance that the majority of residents supports the tax increase.

c. Assuming that 50%of residents support the tax increase, there is an 18%probability that the sample proportion would be 0.527or greater by chance alone.

d. Assuming that more than 50%of residents support the tax increase, there is an 18%probability that the sample proportion would be 0.527or greater by chance alone.

e. Assuming that 50%of residents support the tax increase, there is an 18% chance that the null hypothesis is true by chance alone.

1 A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay \(100 for the upgrade. For the upgrade to be profitable, the company must sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay \)100 for the upgrade.

a. Do the sample data give convincing evidence that more than 20% of the company鈥檚 customers are willing to purchase the upgrade? Carry out an appropriate test at the 伪=0.05significance level.

b. Which would be a more serious mistake in this setting鈥攁 Type I error or a Type II error? Justify your answer.

c. Suppose that 30% of the company鈥檚 customers would be willing to pay $100 for the upgrade. The power of the test to detect this fact is0.60. Interpret this value.

The standardized test statistic for a test of H0:p=0.4versus Ha:pnotequalto0.4isz=2.43This test is

a. not significant at either 伪=0.05or 伪=0.01

b. significant at 伪=0.05but not at伪=0.01

c. significant at伪=0.01but not at 伪=0.05

d. significant at both 伪=0.05and伪=0.01

e. inconclusive because we don鈥檛 know the value of p^

Flu vaccine Refer to ExerciseR9.5. Of the 1000 adults who were given the vaccine, 43 got the flu. Do these data provide convincing evidence to support the company鈥檚 claim?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

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.