Respuesta :
The z-statistic for Brett's data is found to be as given by: Option A: -5.30 (approx).
How to find the value of z-statistic for population mean?
Suppose we're specified that:
- The sample mean = [tex]\overline{x}[/tex]
- The population mean = [tex]\mu[/tex]
- The population standard deviation = [tex]\sigma[/tex]
- The sample size = n
Then the z-statistic for this data is found as:
[tex]Z = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}}[/tex]
For this case, we've got:
- The sample mean = [tex]\overline{x}[/tex] = 295
- The population mean = [tex]\mu[/tex] = 310
- The population standard deviation = [tex]\sigma[/tex] = 20
- The sample size = n = 50
Thus, we get:
[tex]Z = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}} = \dfrac{295 - 310}{20/\sqrt{50}} \approx -5.30[/tex]
Thus, the z-statistic for Brett's data is found to be as given by: Option A: -5.30 (approx).
Learn more about z-statistic here:
https://brainly.com/question/1640298
According to the given data and applying it's formula, the z-statistic is of z = -5.30.
What is the z-statistic formula?
It is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
- [tex]\overline{x}[/tex] is the sample mean.
- [tex]\mu[/tex] is the value tested at the null hypothesis.
- [tex]\sigma[/tex] is the standard deviation of the population.
- n is the sample size.
In this problem, the values of the parameters are given by:
[tex]\overline{x} = 295, \mu = 310, \sigma = 20, n = 50[/tex]
Hence, the z-statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{295 - 310}{\frac{20}{\sqrt{50}}}[/tex]
z = -5.30.
The z-statistic is of z = -5.30.
More can be learned about z-statistic at https://brainly.com/question/26454209
