Question

pre - lab 7 question 5 4.75 points
what type of standard deviation applies for this lab? what is the correct denominator for this?
a population standard deviation (n - 1 in the denominator)
b population standard deviation (n in the denominator)
c sample standard deviation (n - 1 in the denominator)
d sample standard deviation (n in the denominator)

Explanation:

Step1: Recall the definitions

Population standard deviation formula: \(\sigma=\sqrt{\frac{\sum_{i = 1}^{N}(x_{i}-\mu)^{2}}{N}}\), where \(N\) is the population size.
Sample standard deviation formula: \(s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}\), where \(n\) is the sample size.

Step2: Analyze the options

Option A: Incorrect, because population standard deviation has \(n\) (not \(n-1\)) in the denominator.
Option B: Incorrect, because the question is about a lab (usually dealing with samples in a lab - like experiments with a subset of data), not the entire population.
Option C: Correct, in a lab (where we often work with samples), sample standard deviation with \(n - 1\) (Bessel's correction) in the denominator is used.
Option D: Incorrect, sample standard deviation uses \(n-1\) (not \(n\)) in the denominator.

Answer:

C. sample standard deviation (\(n - 1\) in the denominator)