In February 1987 astronomers saw a supernova (S1987A) using optical telescopes.
ID: 3180179 • Letter: I
Question
In February 1987 astronomers saw a supernova (S1987A) using optical telescopes. It was close enough that the explosion's emitted neutrinos should have been detectable. This table gives the number of neutrinos detected in 10-second intervals by the IMB experiment (in a salt mine near Cleveland on February 23, 1987 near the first sight of S1987A). Note the single 9-event interval. Compute the average number of events per interval (both with and without the 9-event interval) Calculate the predicted numbers. (Does it matter which of the averages you use here?) Compute reduced chi squared and its probability both with and without the 9-event interval. Explain clearly the meaning implied by the fact that these two probabilities are vastly different.Explanation / Answer
a) We compute the average number of events per interval with 9-event interval
Total : 2306
Average = 2306/9 = 256.222
We compute the average number of events per interval with 9-event interval
Total : 2306
Average = 2306/10 = 23.06
Again we compute the average number of events per interval without 9-event interval since observated values of 6,7,8 intervals are zero so we omitted the data. That is
Mean = 2306/7 = 329.428
b) Predicted numbers are
With 7 event interval
c)
The chisquare value is calculated as follows
Test statistic
Chisquare value = 3540.26565
d) p-value = 0.000
Here P-value < alpha 0.05, we reject H0
No. of events No. of intervals 0 1042 1 860 2 307 3 78 4 15 5 3 9 1 Total: 2306