Final answer:
The test statistic for the given hypothesis testing scenario where the sample mean is 110, the hypothesized mean is 100, the population standard deviation is 20, and the sample size is 16, is calculated as z = 2.
Step-by-step explanation:
The student's question pertains to computing the value of the test statistic in a hypothesis testing scenario for a single population mean. Given a random sample of 16 observations from a population with a standard deviation of 20 and a sample mean of 110, we need to test the null hypothesis (μ = 100) against the alternative hypothesis (μ > 100). To calculate the test statistic, one would use the formula for the z-test statistic, which is:
Z = (μ - μ0) / (σ / √n)
Where μ is the sample mean, μ0 is the hypothesized population mean, σ is the population standard deviation, and n is the sample size. Following the substitution of known values:
Z = (110 - 100) / (20 / √16)
Z = (10) / (5)
Z = 2
This suggests the test statistic value is 2, and the instructor should use this value to determine whether to reject the null hypothesis.
For this scenario, since the population standard deviation is known, and we assume that the population distribution is normal, a z-test is appropriate. If the population standard deviation was unknown and/or the sample size was small, a t-test might be the appropriate choice.