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Q 105.

Expert-verified
Found in: Page 611

### The Practice of Statistics for AP Examination

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 $1$

See the step by step solution

## Step 1: Given information

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

## Step 2: Calculation

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).