You wish to test the following claim $(H_{a})$ at a significance level of $α = 0.10$ .
$\begin{array}{l} H_{o} : μ = 78.2 \\ H_{a} : μ > 78.2 \end{array}$

You believe the population is normally distributed and you know the standard deviation is $σ = 10.5$ . You obtain a sample mean of $M = 81.1$ for a sample of size $n = 62$ .

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 four decimal places.)
$p -value =$

The $p$ -value is...
- less than (or equal to) $α$

Answer

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Answer

The test statistic is $2.175$

Steps

Step 1 ：Calculate the test statistic using the formula $z = \frac{\bar{x} - μ}{\frac{σ}{\sqrt{n}}}$

Step 2 ：Plug in the given values: $\bar{x} = 81.1$ , $μ = 78.2$ , $σ = 10.5$ , and $n = 62$

Step 3 ：Compute the test statistic: $z = \frac{81.1 - 78.2}{\frac{10.5}{\sqrt{62}}}$

Step 4 ：The test statistic is $2.175$