Respuesta :
The value of the test statistic to test the claim of comparison of average GPA is found to be -0.83 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 (hypothesized)= [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 by:
[tex]s = \dfrac{\sigma}{\sqrt{n}}[/tex]
where [tex]\sigma[/tex] = population standard deviation
For this case, since the sample size is 81 > 30, and we want to compare the mean (population mean) with some hypothesized mean (3.5 here), therefore, we can use one-sample z-test, which has the aforesaid test statistic.
We're provided that:
- n = sample size = 81
- sample mean = [tex]\overline{x}[/tex] = 3.25
- sample standard deviation = s = 0.3
- hypothesized population mean with which comparison is done = [tex]\mu= 3.5[/tex]
Thus, we get:
[tex]z = \dfrac{\overline{x} - \mu}{s} = \dfrac{3.25 - 3.5}{0.3} \approx -0.83[/tex]
Thus, the value of the test statistic to test the claim of comparison of average GPA is found to be -0.83 approximately.
Learn more about one-sample z-test here:
https://brainly.com/question/21477856
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