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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:渭>0.5Ha:x炉=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鈭�0.5070.5(0.5)4040=鈭�0.89;P-value=1鈭�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鈮�0.5

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

Calculating the p-value,=2脳P(Z>|z|)

=2脳P(Z>|0.890|)=0.373

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

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Most popular questions from this chapter

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures

students鈥� attitudes toward school and study habits. Scores range from 0 to 200. The mean score for U.S. college students is about 115. A teacher suspects that older students have better attitudes toward school. She gives the SSHA to an SRS of 45

of the over 1000 students at her college who are at least 30 years of age.

The z statistic for a test of H0 :p = 0.4 versus Ha : p > 0.4 is z = 2.43. This 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 藛p .

Heat through the glass How well materials conduct heat matters when designing houses, for example. Conductivity is measured in terms of watts of heat power transmitted per square meter of surface per degree Celsius of temperature difference on the two sides of the material. In these units, glass has conductivity about 1. The National Institute of Standards and Technology provides exact data on properties of materials. Here are measurements of the heat conductivity of 11randomly selected pieces of a particular type of glass:

1.111.071.111.071.121.081.081.181.181.181.12

Is there convincing evidence that the conductivity of this type of glass is greater than 1? Carry out a test to help you answer this question.

We want to be rich In a recent year, 73 % of first-year college students responding to a national survey identified "being very well-off financially" as an important personal goal. A state university finds that 132 of an SRS of 200 of its first-year students say that this goal is important. Is there good evidence that the proportion of all first-year students at this university who think being very well-off is important differs from the national value, 73 %? Carry out a test at the 伪=0.05 significance level to help answer this question.

You read that a statistical test at the 伪=0.01 level has a probability of 0.14 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative?
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