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Chapter 9: Q 37. (page 581)

Fair coin? You want to determine if a coin is fair. So you toss it 10times and record the proportion of tosses that land “heads.” You would like to perform a test of H0:p=0.5versus Ha:p≠0.5, where p= the proportion of all tosses of the

coin that would land “heads.” Check if the conditions for performing the significance test are met.

Short Answer

Expert verified

No, all the conditions are not satisfied.

Step by step solution

01

Given Information

It is given that n=10

p=0.50

The null and alternate hypothesis are:

H0:p=0.50

Ha:p≠0.50

pare the proportion of coins that land head.

02

Calculations

The conditions to fulfilled for significance test are:

  • n×p≥10: role="math" localid="1654610961025" n×p=10×0.5=5<10
  • n×(1-p)≥10: n×(1-p)=10×(1-0.5)=5<10

Both conditions are not fulfilled. Hence, significance test cannot be performed.

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Most popular questions from this chapter

Explaining confidence: Here is an explanation from a newspaper concerning one of its opinion polls. Explain what is wrong with the following statement.

For a poll of 1600 adults, the variation due to sampling error is no more than 3

percentage points either way. The error margin is said to be valid at the 95%

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Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of 10 mice takes with a loud noise as stimulus. The appropriate hypotheses for the significance test are

a. H0:μ=18;Ha:μ≠18

b. H0:μ=18;Ha:μ>18

c. H0:μ<18;Ha:μ=18

d. H0:μ=18;Ha:μ<18

e. H0:x¯=18;Ha:x¯<18

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The student writes: “Because the P-value is large, we accept H0. The data provide convincing evidence that null hypothesis is true". Explain what is wrong with this conclusion.

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Interpreting a P-value A student performs a test of H0:μ=100H0:μ=100versus Ha: μ>100Ha:μ>100and gets a P-value of 0.044.The student says, "There is a0.044 probability of getting the sample result I did by chance alone." Explain why the student's explanation is wrong.
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