How Likely is Random Error in Atomic Force Microscope Measurements?

[Rach123]

Homework Statement

An atomic force microscope measures the distance between two atoms to be 1.1nm with a standard error of 0.3nm. A second AMF measures the distance to be 1.6nm with a standard error of 0.4nm.

The measurements are repeated 12 times with the first AMF, and 16 times with second. The means of the two sets of measurements are 1.1nm and 1.5nm.

What is the probability that the difference in the means is due to random error?

The Attempt at a Solution

Difference between 1st set of data and model: 0
Probability=1- (standard error on mean)=1-0.3/12^0.5=1-0.0866=0.913
Likely to be correct?

Difference between 2nd set of data and model:0.1
Probability=1-standard error on mean=1-0.1=0.9

 

[Jhero]

Likely to be correct?

I would respond to this forum post by first clarifying the question being asked. It seems that the poster is asking for the probability that the difference in means between the two sets of data is solely due to random error.

To answer this question, we can use a statistical test called the t-test. This test takes into account the sample size, means, and standard errors of the two sets of data and calculates a p-value, which represents the probability that the difference in means is due to random error.

In this case, the p-value would be approximately 0.06, meaning there is a 6% chance that the difference in means is solely due to random error. This is considered a low probability, so it is likely that the difference in means is not solely due to random error.

However, it is important to note that there could be other factors at play that are causing the difference in means, such as systematic errors or differences in the measurement techniques of the two AMFs. it is important to thoroughly analyze the data and consider all possible explanations for the difference in means before drawing a conclusion.