Question

An educational researcher claims that the average GPA of graduate students at FIU is less than 3.5 . To test his claim he collected data on 81 graduate students . The sample mean GPA was 3.25 with a standard deviation of 0.3 . What is the value of the test statistic to test this claim

Answer 1

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 = $\overline{x}$
• Sample size = n
• Population mean (hypothesized)= $\mu$
• 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 by:

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

where $\sigma$ = 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 = $\overline{x}$ = 3.25
• sample standard deviation = s  = 0.3
• hypothesized population mean with which comparison is done = $\mu= 3.5$

Thus, we get:

$z = \dfrac{\overline{x} - \mu}{s} = \dfrac{3.25 - 3.5}{0.3} \approx -0.83$

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

#SPJ1