Problem

Claim: The mean pulse rate (in beats per minute) of adult males is equal to $68.8 \mathrm{bpm}$. For a random sample of 126 adult males, the mean pulse rate is $67.9 \mathrm{bpm}$ and the standard deviation is $11.1 \mathrm{bpm}$. Complete parts (a) and (b) below.
a. Express the original claim in symbolic form.
bpm
(Type an integer or a decimal. Do not round.)

Answer

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Answer

\(\boxed{-0.91}\) is the test statistic.

Steps

Step 1 :The original claim can be expressed in symbolic form as \(\mu = 68.8\), where \(\mu\) represents the mean pulse rate of adult males in beats per minute.

Step 2 :\(\mu = 68.8\) bpm is the original claim in symbolic form.

Step 3 :To find the test statistic, we can use the formula for a z-score, which is \((\bar{x} - \mu) / (\sigma / \sqrt{n})\), where \(\bar{x}\) is the sample mean, \(\mu\) is the population mean, \(\sigma\) is the standard deviation, and \(n\) is the sample size.

Step 4 :Given that \(\bar{x} = 67.9\), \(\mu = 68.8\), \(\sigma = 11.1\), and \(n = 126\), we can substitute these values into the z-score formula to find the test statistic.

Step 5 :The test statistic (z-score) is approximately -0.91. This value indicates how many standard deviations the sample mean is below the population mean.

Step 6 :\(\boxed{-0.91}\) is the test statistic.

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