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Q 105.

Expert-verifiedFound in: Page 611

Book edition
6th

Author(s)
Daren Starnes, Josh Tabor

Pages
837 pages

ISBN
9781319113339

After checking that conditions are met, you perform a significance test of ${H}_{0}:\mu =1$ versus ${H}_{a}:\mu \ne 1$ You obtain a $P-$value of $0.022$ Which of the following must be true?

a. A $95\%$ confidence interval for ${\mu}^{\mu}$ will include the value $1$

b. A $95\%$ confidence interval for ${\mu}^{\mu}$ will include the value $0.022$

c. A $99\%$ confidence interval for ${\mu}^{\mu}$ will include the value $1$

d. A $99\%$ confidence interval for ${\mu}^{\mu}$ will include the value $0.022$

e. None of these is necessarily true.

The correct option is (c) A $99\%$ confidence interval for ${\mu}^{\mu}$ will include the value $1$

${H}_{0}:\mu =1\phantom{\rule{0ex}{0ex}}{H}_{a}:\mu \ne 1\phantom{\rule{0ex}{0ex}}P=0.022$

The null hypothesis is rejected if the $P-$value is less than the significance level.

$P<0.05=5\%reject{H}_{0}\phantom{\rule{0ex}{0ex}}P>0.01=1\%=failstoreject{H}_{0}$

A significance test at the $5\%$ significance level equates to a $95$ percent confidence interval.

A significance test at the $1\%$ significance level equates to a $99$ percent confidence interval.

There is no one in $95\%$ of the confidence interval.

There are $1$ in the $95\%$ confidence interval.

So correct option is (c).

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