Q1-15BSC - Elementary Statistics

Question

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”

Step-by-Step Solution

Answer

The value of the test statistic (z-score) is equal to 0.656.

Step 1: Given Information

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.

Step 2: Hypotheses

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.

\({H_1}:\mu  \ne 69\)

Step 3: Test statistic

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

 

The value of the sample mean is equal to \(\bar x = 69.6\)

 

The given value of the mean pulse rates of adult males is 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:

 

\(\begin{array}{c}z = \frac{{\bar x - \mu }}{{\frac{\sigma }{{\sqrt n }}}}\\ = \frac{{69.6 - 69}}{{\frac{{11.3}}{{\sqrt {153} }}}}\\ = 0.656\end{array}\)

 

Thus, the test statistic is equal to 0.656.