Test Statistics. In Exercises 13–16, refer to the exercise identified and find the value of the test statistic. (Refer to Table 8-2 on page 362 to select the correct expression for evaluating the test statistic.)

Exercise 7 “Pulse Rates”

For a sample of 153 adult males, the mean pulse rate is equal to 69.6 bpm, and the standard deviation is equal to 11.3 bpm.

It is claimed that the mean pulse rate of adult males is equal to 69 bpm.

Corresponding to the given claim, the following hypotheses are set up:

Null hypothesis: The mean pulse rate of adult males is equal to 69 bpm.

$H_0:\mu =69$

Alternative hypothesis: The mean pulse rate of adult males is not equal to 69 bpm.

$H_1:\mu \ne 69$

Since the claim involves testing the equality of the sample mean with a hypothesized value, the test statistic used will be the z-score.

The value of the sample mean is equal to$\overline{x}=69.6$

The given value of the mean pulse rates of adult malesis supposed to be equal to 69.

Thus,$\mu =69$ .

The sample size (n) is equal to 153.

The value of the test statistic is computed below:

$$\begin{gathered} z=\frac{\overline{x}-\mu }{\frac{\sigma }{\sqrt{n}}} \\ =\frac{69.6-69}{\frac{11.3}{\sqrt{153}}} \\ =0.656 \end{gathered}$$

Thus, the test statistic is equal to 0.656.