You suspect that there are cosmic rays influencing your chickens and you want to
ID: 3221279 • Letter: Y
Question
You suspect that there are cosmic rays influencing your chickens and you want to try and see if you can quantify the cosmic rays in your chicken coop. Suppose you use a Geiger counter to count the cosmic radiation in your coop, and you count these over 100 time intervals and get the following data:
Can you say you have a normal distribution of cosmic rays on your chicken coop?
Identify the type of problem and statistics to be used and justify/explain your answer.
counts in interval occurrences 0 6 1 18 2 28 3 21 4 17 5 7 6 1 7 2 8 or more 0Explanation / Answer
I am solving this problem using MInitab software
Use Goodness-of-Fit Test for Poisson to test the hypotheses:
H0: Data follow a Poisson distribution
H1: Data do not follow a Poisson distribution
MTB > PGoodness 'counts in interval';
SUBC> Frequencies 'occurrences';
SUBC> GBar;
SUBC> GChiSQ;
SUBC> Pareto;
SUBC> RTable.
Goodness-of-Fit Test for Poisson Distribution
Data column: counts in interval
Frequency column: occurrences
Poisson mean for counts in interval = 2.6
counts in Poisson Contribution
interval Observed Probability Expected to Chi-Sq
0 6 0.074274 7.4274 0.274304
1 18 0.193111 19.3111 0.089019
2 28 0.251045 25.1045 0.333968
3 21 0.217572 21.7572 0.026353
4 17 0.141422 14.1422 0.577500
5 7 0.073539 7.3539 0.017035
>=6 3 0.049037 4.9037 0.739058
N N* DF Chi-Sq P-Value
100 0 5 2.05724 0.841
1 cell(s) (14.29%) with expected value(s) less than 5.
Chart of Observed and Expected Values
Chart of Contribution to the Chi-Square Value by Category
Interpreting the results
Minitab calculates each category's contribution to the chi-square value as the square of the difference in the observed and expected values for a category divided by the expected value for that category. The largest difference between the observed and expected value and is the highest contributor to the chi-square statistic . However, the contribution is not enough to reject the null hypothesis . If you choose an a-level of 0.05, the p-value for this test is 0.841, which is greater than 0.05. Therefore, we can conclude that we do not have enough evidence to reject that thegiven data set follow a Poisson distribution.
Note
The chi-square test is an approximate test and the test result may not be valid when the expected value for a category is less than 5. If one or more categories have expected values less than 5, you can combine them with adjacent categories to achieve the minimum required expected value.
Note
The chi-square test is an approximate test and the test result may not be valid when the expected value for a category is less than 5. If one or more categories have expected values less than 5, you can combine them with adjacent categories to achieve the minimum required expected value.
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