Chapter 9.3, Problem 105E

To determine

To find : best answer for given statement “ after checking that conditions are met, you perform a significance test of $H0:\mu =1$ versus $H_a:\mu \ne 1$ . You obtain a $P-$ value of $0.022$ .

Answer to Problem 105E

Option (C) is correct that is A $99\%$ confidence interval for $\mu$ will include the value $1$ .

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Explanation of Solution

Given information :

1. A $95\%$ confidence interval for $\mu$ will include the value $1$ .
2. A $95\%$ confidence interval for $\mu$ will include the value $0.022$ .
3. A $99\%$ confidence interval for $\mu$ will include the value $1$ .
4. A $99\%$ confidence interval for $\mu$ will include the value $0.022$ .
5. None of these is necessarily true.

  $H0:\mu =1$

  $H_a:\mu \ne 1$

  $P=0.022$

If the $P-$ value is smaller than the significance level, then null hypothesis is rejected.

  $P<0.05=5\%$ reject $H_0$

  $P>0.01=1\%=$ fails to reject $H_0$ .

A $95\%$ confidence interval corresponds with a significance test at the $5\%$ significance level.

A $99\%$ confidence interval corresponds with a significance test at the $1\%$ significance level.

If the significance test was significant, then the interval does not contain the value which is mentioned in hypotheses.

  $95\%$ confidence interval does not contain $1$ .

  $99\%$ confidence interval contains $1$ .

So correct option is (c).