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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

A change is made that should improve student satisfaction with the parking situation at your school. Right now, 37% of students approve of the parking that鈥檚 provided. The null hypothesis H0:p^=0.37is tested against the alternativeHd:p^鈮�0.37.

The health director of a large company is concerned about the effects of stress on the company鈥檚 middle-aged male employees. According to the National Center for Health Statistics, the mean systolic blood pressure for males 35 to 44 years of age is 128. The health director examines the medical records of a random sample of 72 male employees in this age group. The Minitab output below displays the results of a significance test and a confidence interval.

1. Do the results of the significance test allow us to conclude that the mean blood pressure for all the company鈥檚 middle-aged male employees differs from the national average? Justify your answer.

2. Interpret the 95% confidence interval in context. Explain how the confidence interval leads to the same conclusion as in Question 1.

In planning a study of the birth weights of babies whose mothers did not see a doctor

before delivery, a researcher states the hypotheses as

H0:x炉=1000gramsHa:x炉<1000grams

A college professor suspects that students at his school are getting less than 8 hours of sleep a night, on average. To test his belief, the professor asks a random sample of 28 students, 鈥淗ow much sleep did you get last night?鈥� Here are the data (in hours): 96868866.56794345611636610784.5977

Do these data provide convincing evidence in support of the professor鈥檚 suspicion? Carry out a significance test at the a=0.05level to help answer this question.

Sweetening colas Cola makers test new recipes for loss of sweetness during storage. Trained tasters rate the sweetness before and after storage. From experience, the population distribution of sweetness losses will be close to Normal. Here are the sweetness losses (sweetness before storage minus sweetness after storage) found by tasters from a random sample of 10batches of a new cola recipe:

2.00.40.72.0-0.42.2-1.31.21.12.3

Are these data good evidence that the cola lost sweetness? Carry out a test to help you answer this question.
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