Question

A researcher collated data on Americans’ leisure time activities. She found the mean number of hours spent watching television each weekday to be 2. 7 hours with a standard deviation of 0. 4 hours. Jonathan believes that his football team buddies watch less television than the average American. He gathered data from 15 football teammates and found the mean to be 2. 3. Which of the following shows the correct z-statistic for this situation? -3. 87 -0. 26 3. 23 5. 22.

Answer 1

The value of the z statistic for the considered data is given by: Option A: -3.87 approximately.

How to find the z score (z statistic) for the sample mean?

If we're given that:

• Sample mean = $\overline{x}$
• Sample size = n
• Population mean = $\mu$
• Sample standard deviation = s

Then, we get:

$z = \dfrac{\overline{x} - \mu}{s}$

If the sample standard deviation is not  given, then we can estimate it(in some cases) by:

$s = \dfrac{\sigma}{\sqrt{n}}$

where $\sigma$population standard deviation

For this case, we're specified that:

• Sample mean = $\overline{x}$ = 2.3
• Sample size = n = 15
• Population mean = $\mu$  = 2.7
• Population standard deviation = $\sigma$ = 0.4

Thus, the value of the z-statistic is evaluated as:

$z = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}} = \dfrac{2.3- 2.7}{0.4/\sqrt{15}} \approx -3.87$

Thus, the value of the z statistic for the considered data is given by: Option A: -3.87 approximately.

Learn more about z statistic here:

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