Answer :
Final answer:
The most appropriate statistical test for this particular study would be the z-Test.
Explanation;
Given the problem's context, we can observe that we're comparing the sample mean (M=1400) of Dr. Garbin's students to a population mean (u=1200). Additionally, we're provided with the population standard deviation (o=150).
To determine the correct statistical test, let's understand what each of these tests is used for:
1. A z-Test is employed when we're comparing a sample mean to a population mean, and we know the population standard deviation.
2. A Paired Samples t Test is applied when we're comparing the means of the same group at two different instances of time.
3. A Single-Sample t Test is employed when we're comparing the sample mean to a population mean, but we do not know the population standard deviation.
4. An Independent Samples t Test is applied when we're comparing the means of two different groups.
Considering our case, we're comparing a single sample mean with a known population mean and the population standard deviation's value is also known to us. With such conditions laid out, the most appropriate statistical test for this particular study would be the z-Test.
Why? Because one of the main conditions for applying the z-test - knowing the population's standard deviation - is fulfilled. Hence, despite dealing with a relatively small sample size (N - 35), the known standard deviation of the population allows us to go ahead with the z-Test.
In practical terms and for future reference, when population standard deviation is known, z-Test is predominantly preferred; otherwise, when only the sample's statistics are known, we go for the t-tests.
To learn more about Z-test, visit;
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