Testing Claims
You wish to test the following claim $(H_{a})$ at a significance level of $α = 0.002$ .
$\begin{array}{l} H_{o} : p = 0.9 \\ H_{a} : p > 0.9 \end{array}$
You obtain a sample of size $n = 122$ in which there are 121 successful observations.
What is the test statistic for this sample? (Report answer accurate to three decimal places. test statistic $=$
What is the $p$ -value for this sample? (Report answer accurate to three decimal places.)
$p -$ value $=$
The p-value is...
less than (or equal to) $α$
greater than $α$
This test statistic leads to a decision to...
reject the null
accept the null

Answer

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Answer

$p$ -value $= P (Z > 3.080) \approx 0.001$

Steps

Step 1 ： $\hat{p} = \frac{121}{122}$

Step 2 ： $z = \frac{\hat{p} - p_{0}}{\sqrt{\frac{p_{0} (1 - p_{0})}{n}}} = \frac{\frac{121}{122} - 0.9}{\sqrt{\frac{0.9 (1 - 0.9)}{122}}} \approx 3.080$

Step 3 ： $p$ -value $= P (Z > 3.080) \approx 0.001$

Answer

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