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Q.1

Expert-verifiedFound in: Page 597

Book edition
4th

Author(s)
David Moore,Daren Starnes,Dan Yates

Pages
809 pages

ISBN
9781319113339

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are

a).${H}_{0}:\hat{p}=0.5;{H}_{a}:\hat{p}>0.5$

(b) ${H}_{0}:p=0.5;{H}_{a}:p>0.5$

(c) ${H}_{0}:p=0.5;{H}_{a}:p<0.5$

(d) ${H}_{0}:p=0.5;{H}_{a}:p\ne 0.5$

(e) ${H}_{0}:p>0.5;{H}_{a}:p=0.5$

The null and alternative hypotheses you would use to test this claim are (b) ${H}_{0}:p=0.5;{H}_{a}:p>0.5$

The hypotheses are statements about the population parameter:

$p$ : population proportion.

$\mu :$ population mean.

$\sigma :$ population standard deviation.

The null hypothesis states that the population parameter is equal to the value mentioned in the claim:

${H}_{0}:p=50\%=0.50$The alternative hypothesis states the opposite of the null hypothesis (according to the claim):

${H}_{a}:p>0.50$Therefore, the correct answer is (B).

Eye black Athletes performing in bright sunlight often smear black grease under their eyes to reduce glare. Does cye black work? In one experiment, 16 randomly selected student subjects took a test of sensitivity to contrast after 3 hours facing into bright sun, both with and without eye black. Here are the differences in sensitivity, with eye black mines without eye black:

0.07 | 0.64 | -0.12 | -0.05 | -0.18 | 0.14 | -0.16 | 0.03 |

0.05 | 0.02 | 0.43 | 0.24 | -0.11 | 0.28 | 0.05 | 0.29 |

We want to know whether cye black increases sensitivity an the average.

(a) State hypotheses, Be sure to define the parameter.

(b) Check conditions for carrying out a significance test.

(c) The$Pvalue$ of the test is $0.047$. Interpet this value in context.

- Interpret a Type l error and a Type ll error in context, and give the consequences of each.

- Understand the relationsonship between the significance level at a test P(Type li error), and power.

Fonts and reading ease Does the use of fancy type fonts slow down the reading of text on a computer screen? Adults can read four paragraphs of text in the common Times New Roman font in an average time of $22$ seconds. Researchers asked a random sample of $24$ adults to read this text in the omate font named Gigi. Here are their times, in seconds:

23.2 | 21.2 | 28.9 | 27.7 | 29.1 | 27.3 | 16.1 | 22.6 | 25.6 | 34.2 | 23.9 | 26.8 |

20.5 | 34.3 | 21.4 | 32.6 | 26.2 | 34.1 | 31.5 | 24.6 | 23.0 | 28.6 | 24.4 | 28.1 |

Do these data provide good evidence that the mean reading time for Gigi is greater than $22$seconds? Carry out an appropriate test to help you answer this question.

- Use a confidence interval to draw a conclusion for a two-sided test about a population mean.

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