Preliminary Study: Detecting Cosmic Muons with Geiger-Muller Tube Pair

Since the completion of the coincident system recently, a test was planned for it to find out if a block of lead plates placed before the GM tube pair, will the coincident counter give different count rates?  The basis of this test was:

1. Could lead attenuate low energy secondary beta particles, thus reducing the coincident counts per hour (CPH)? 

2. Could the presence of lead increases the collision probability of whatever passing though the metal (electromagnetic component or muons) which induces cascade, thus increase the chance of coincidence count, which leads to higher CPH?  

The test was conducted where the electronics of coincident system and tube positions unchanged, but two sets of data was taken. One was when two GM tubes are left alone and while the other has a 13.0 mm fishing lead plates almost in contact to the upper GM tube (photo below). 

A total of 16 hours of data was collected for each set and are shown as below:

WITHOUT 13 MM LEAD PLATES (Left Figure)

Data [CPH]: 39, 47, 50, 49, 43, 46, 49, 48, 41, 49, 47, 39, 44, 30, 42, 54 (n=16)

Mean: 44.8125          Median: 46.5

Unbiased Standard Deviation: 5.7645

Simple reading: (45 ± 12) CPH

WITH 13 MM LEAD PLATES (Right Figure)

Data [CPH]: 46, 42, 28, 50, 38, 34, 47, 40, 77, 46, 36, 30, 44, 48, 34, 43 (n=16)

Mean: 42.6875          Median: 42.5

Unbiased Standard Deviation: 11.2648

Simple reading: (43 ± 25) CPH

Since n < 30, T-distribution was used to conduct a hypothesis testing. The test was to determine if there is a difference between the average or "mean" of the population (i.e. data using lead vs. data without lead) where:

Null Hypothesis: There is no difference between the population mean.

 Alternative hypothesis: There is a difference between the population mean.

The test statistics was computed using 2 sample Welch's T-test formula assuming unequal variance which gives a test statistics of  0.6717 with a degree-of-freedom 22. The resulting P-value is 0.5088. Thus, the null hypothesis is not rejected (insufficient evidence to accept alternative hypothesis).

In conclusion, there is no statistical significance in the difference between the population mean (i.e. with lead vs. without lead) within a short acquisition time. Experimentally, it makes no difference on the rate of photography regardless of the presence of a lead target.