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Testing Claims
You wish to test the following claim $(H_{a})$ at a significance level of $α = 0.002$ .
$\begin{array}{l} H_{o} : p = 0.28 \\ H_{a} : p \neq 0.28 \end{array}$
You obtain a sample of size $n = 440$ in which there are 106 successful observations.
What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic $= - 1.826 ✓ σ^{ς}$
What is the $p$ -value for this sample? (Report answer accurate to three decimal places.)
$p -value = 0.2409 x$
The $p$ -value is...
less than (or equal to) $α$
greater than $α$

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Answer

3. Calculate $p$ -value: $p - value = 2 \cdot P (Z > | - 1.826 |) = 2 \cdot P (Z > 1.826) = 0.0676$

Steps

Step 1 ：1. Calculate $\hat{p}$ : $\hat{p} = \frac{106}{440} = 0.2409$

Step 2 ：2. Calculate test statistic: $z = \frac{\hat{p} - p_{0}}{\sqrt{\frac{p_{0} (1 - p_{0})}{n}}} = \frac{0.2409 - 0.28}{\sqrt{\frac{0.28 (1 - 0.28)}{440}}} = - 1.826$

Step 3 ：3. Calculate $p$ -value: $p - value = 2 \cdot P (Z > | - 1.826 |) = 2 \cdot P (Z > 1.826) = 0.0676$

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