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Sagot :
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 = [tex]\overline{x}[/tex]
- Sample size = n
- Population mean = [tex]\mu[/tex]
- Sample standard deviation = s
Then, we get:
[tex]z = \dfrac{\overline{x} - \mu}{s}[/tex]
If the sample standard deviation is not given, then we can estimate it(in some cases) by:
[tex]s = \dfrac{\sigma}{\sqrt{n}}[/tex]
where [tex]\sigma[/tex]population standard deviation
For this case, we're specified that:
- Sample mean = [tex]\overline{x}[/tex] = 2.3
- Sample size = n = 15
- Population mean = [tex]\mu[/tex] = 2.7
- Population standard deviation = [tex]\sigma[/tex] = 0.4
Thus, the value of the z-statistic is evaluated as:
[tex]z = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}} = \dfrac{2.3- 2.7}{0.4/\sqrt{15}} \approx -3.87[/tex]
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:
https://brainly.com/question/27003351
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