Question

Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students' lab measurements is σ = 13 milligrams. Juan repeats the measurement 5 times and records the mean x¯¯¯ of his 5 measurements. (a) What is the standard deviation of Juan's mean result? (That is, if Juan kept on making 5 measurements and averaging them, what would be the standard deviation of all his x¯¯¯′s?) (b) How many times must Juan repeat the measurement to reduce the standard deviation of x¯¯¯ to 2.6?

Answer 1

Answer:

a) 5.81

b) 25            

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 5

Population standard deviation, σ = 13 milligrams

a) standard deviation of Juan's mean result

$\text{Standard error} = \dfrac{\sigma}{\sqrt{n}} = \dfrac{13}{\sqrt{5}} = 5.81$

5.81 is the standard deviation of Juan's mean result.

b) sample size such that the standard deviation reduces to 2.6

$\text{Standard error} = \dfrac{\sigma}{\sqrt{n}}\\\\\Rightarrow \dfrac{13}{\sqrt{n}} = 2.6\\\\\Rightarrow \sqrt{n} = \dfrac{13}{2.6} = 5\\\\\Rightarrow n = 25$

Thus, Juan has to repeat the experiment 25 times to reduce the standard deviation to 2.6