Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Q.48 (page 563)

The French naturalist Count Buffon (1707-1788) tossed a coin 4040 times. He got 2048 heads. That's a bit more than one-half. Is this evidence that Count Buffon's coin was not balanced? To find out, Luisa decides to perform a significance test. Unfortunately, she made a few errors along the way. Your job is to spot the mistakes and correct them.

H0:μ>0.5Ha:x¯=0.5

- Independent 4040(0.5)=2020 and 4040(1-0.5)=2020 are both at least 10 .

- Normal There are at least 40,400 coins in the world.

t=0.5−0.5070.5(0.5)4040=−0.89;P-value=1−0.1867=0.8133

Reject H0because the P-value is so large and conclude that the coin is fair.

Short Answer

Expert verified

The coin is fair as there is enough evidence.

Step by step solution

01

Introduction

the hypothesis to be a scientific hypothesis, the scientific technique requires that one can test it. Scientists for the most part base scientific speculations on previous observations that can't satisfactorily be explained with the available scientific theories

02

Explanation 

coins have been tossed n= 4040times

Head obtained x = 2048

Sample proportion role="math" localid="1652936572256" p-=xn=20484040=0.507

Calculating the null and alternative hypotheses,

H0:p=0.5H0:p≠0.5

Using, Z=p-−p0p01−p0n=0.507−0.500.50(0.50)4040=0.890

Calculating the p-value,=2×P(Z>|z|)

=2×P(Z>|0.890|)=0.373

The p-value is greater than the significance level hence coin is fair as there is enough evidence.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Improving health A large company's medical director launches a health promotion campaign to encourage employees to exercise more and eat better foods. One measure of the effectiveness of such a program is a drop in blood pressure. The director chooses a random sample of 50employees and compares their blood pressures from physical cams given before the campaign and again a year later. The mean change (after - before) in systolic blood pressure for these 50employees is -6and the standard deviation is 19.8.

(a) Do these data provide convincing evidence of an average decrease in blood pressure among all of the company's employees during this year? Carry out a test at the α=0.05significance level.

(b) Can we conclude that the health campaign caused a decrease in blood pressure? Why or why not?

A change is made that should improve student satisfaction with the parking situation at a local high school. Right now, 37% of students approve of the parking that’s provided. The null hypothesis H0:p>0.37is tested against the alternativeHa:p=0.37.

A government report says that the average amount of money spent per U.S. household per week on food is about \(158. A random sample of 50households in a small city is selected, and their weekly spending on food is recorded. The Minitab output below shows the results of requesting a confidence interval for the population mean M. An examination of the data reveals no outliers.

(a) Explain why the Normal condition is met in this case.

(b) Can you conclude that the mean weekly spending on food in this city differs from the national figure of\)158? Give appropriate evidence to support your answer.

A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of one inch could be increased by

(a) using only volunteers from the basketball team in the experiment.

(b) using A=0.01 instead of A=0.05.

(c) using A=0.05 instead of A=0.01.

(d) giving the drug to 25 randomly selected students instead of 50.

(e) using a two-sided test instead of a one-sided test.

The P-value for a two-sided test of the null hypothesis H0:μ=10is 0.06

(a) Does the95%confidence interval forMinclude 10? Why or why not?

(b) Does the 90%confidence interval forMinclude 10? Why or why not

See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Applied Mathematics

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.

Sign-up for free