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57

Expert-verifiedFound in: Page 564

Book edition
4th

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

Pages
809 pages

ISBN
9781319113339

After once again losing a football game to the archrival, a college’s alumni association conducted a survey to see if alumni were in favor of firing the

coach. An SRS of 100 alumni from the population of all living alumni was taken, and 64 of the alumni in the sample were in favor of firing the coach.

Suppose you wish to see if a majority of living alumni are in favor of firing the coach. The appropriate test statistic is

a. $z=\frac{0.64-0.5}{\sqrt{\frac{0.64(0.36)}{100}}}$

b.$t=\frac{0.64-0.5}{\sqrt{\frac{0.64(0.36)}{100}}}$

c.$z=\frac{0.64-0.5}{\sqrt{\frac{0.5(0.5)}{100}}}$

d.$z=\frac{0.64-0.5}{\sqrt{\frac{0.64(0.36)}{64}}}$

e.$z=\frac{0.5-0.64}{\sqrt{\frac{0.5(0.5)}{100}}}$

Option a is correct

The test statistic for the population proportion is as follows:

$z=\frac{p-\widehat{p}}{\sqrt{\frac{p\left(1-p\right)}{100}}}$

where $p=0.64$, role="math" localid="1654256041572" $\widehat{p}=0.5$ and $n=100$.

Substitute the respective values in the test statistic.

$\begin{array}{c}z=\frac{0.64-0.5}{\sqrt{\frac{0.64\left(1-0.64\right)}{100}}}\\ =\frac{0.64-0.5}{\sqrt{\frac{0.64\times 0.36}{100}}}\end{array}$

So, option a is the correct option.

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.

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