j) a researcher is conducting a study of qcc ...
j) a researcher is conducting a study of qcc students with a sample size of n = 100. which of the following best describes the procedure he should use? a) he can only use t procedures because his sample is relatively small. b) he can only use z procedures because his sample is relatively large. c) it does not matter if he uses t or z procedures because they are almost identical on a large n.
Answer
# Explanation:
## Step1: Define sample - size criteria
In general, a sample size of \(n = 100\) is considered relatively large. When the sample size \(n\) is large (\(n\geq30\) is a common rule - of - thumb), the sampling distribution of the sample mean is approximately normal.
## Step2: Analyze \(t\) and \(z\) procedures
For large samples, the \(z\) - procedures are appropriate when the population standard deviation \(\sigma\) is known. The \(t\) - procedures are used when the population standard deviation \(\sigma\) is unknown and is estimated by the sample standard deviation \(s\). However, as the sample size \(n\) gets large, the \(t\) - distribution approaches the standard normal (\(z\)) distribution. But the key here is that for a relatively large sample size like \(n = 100\), the \(z\) - procedures are more appropriate when the population standard deviation is known.
# Answer:
b) He can only use \(z\) procedures because his sample is relatively large.