Problem

Claim: The mean pulse rate (in beats per minute) of adult males is equal to $69 \mathrm{bpm}$. For a random sample of 149 adult males, the mean pulse rate is $67.7 \mathrm{bpm}$ and the standard deviation is $10.9 \mathrm{bpm}$. Find the value of the test statistic.
The value of the test statistic is
(Round to two decimal places as needed.)

Answer

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Answer

\(\boxed{\text{Final Answer: The value of the test statistic is approximately -1.46.}}\)

Steps

Step 1 :Given that the sample mean \(\bar{X} = 67.7\), the population mean \(\mu = 69\), the standard deviation \(\sigma = 10.9\), and the sample size \(n = 149\).

Step 2 :The test statistic for a hypothesis test about a population mean can be calculated using the formula: \[Z = \frac{\bar{X} - \mu}{\sigma / \sqrt{n}}\]

Step 3 :Substitute the given values into the formula: \[Z = \frac{67.7 - 69}{10.9 / \sqrt{149}}\]

Step 4 :Solving the above expression gives the value of the test statistic as approximately -1.46.

Step 5 :\(\boxed{\text{Final Answer: The value of the test statistic is approximately -1.46.}}\)

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