Questions: Testing: Ha: μ>21.46 Your sample consists of 43 subjects, with a mean of 23.4 and standard deviation of 4.08. Calculate the test statistic, rounded to 2 decimal places.

Testing: Ha: μ>21.46 Your sample consists of 43 subjects, with a mean of 23.4 and standard deviation of 4.08. Calculate the test statistic, rounded to 2 decimal places.
Transcript text: Testing: \[ H_{a}: \mu>21.46 \] Your sample consists of 43 subjects, with a mean of 23.4 and standard deviation of 4.08. Calculate the test statistic, rounded to 2 decimal places. $\square$
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Solution

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Solution Steps

Step 1: Calculate the Standard Error

To calculate the Standard Error \(SE\), we use the formula:

\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{4.08}{\sqrt{43}} \approx 0.62 \]

Step 2: Calculate the Test Statistic

The test statistic \(Z_{test}\) is calculated using the formula:

\[ Z_{test} = \frac{\bar{x} - \mu_0}{SE} = \frac{23.4 - 21.46}{0.62} \approx 3.12 \]

Step 3: Determine the P-value

For a right-tailed test, the P-value is calculated as:

\[ P = 1 - T(z) \approx 0.0 \]

Final Answer

The test statistic is approximately \(Z_{test} = 3.12\).

Thus, the final answer is \\(\boxed{3.12}\\).

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