If we have a sample of 12 drawn from a normal population, then we would use as our test statistic
A) z0 with 11 degrees of freedom
B) t0 with 12 degrees of freedom
C) z0 with 12 degrees of freedom
D) t0 with 11 degrees of freedom
To determine the appropriate test statistic for a sample drawn from a normal population, we typically consider two factors: the population variance (known or unknown) and the sample size.
In this case, if the population variance is known, we would use a z-test. However, the question does not provide information about the population variance, so we should assume it is unknown.
When the population variance is unknown, we use the t-test, which is appropriate for smaller sample sizes. The degrees of freedom for a t-distribution are calculated as the sample size minus one.
In this question, we have a sample of 12, so the degrees of freedom for the t-distribution would be 12 - 1 = 11. Thus, the correct answer is:
D) t0 with 11 degrees of freedom
The correct answer is D) t0 with 11 degrees of freedom.
When we have a sample of 12 drawn from a normal population and we are comparing it to a known population mean, we use the t-test. The test statistic for the t-test is calculated as (x̄ - μ) / (s / √n), where x̄ is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
For this scenario with a sample size of 12, we use the t-distribution and degrees of freedom given by (n - 1), which is (12 - 1) = 11. Therefore, the correct test statistic is t0 with 11 degrees of freedom (option D).