Question

Please show all steps! I am not supposed to use excel or a calculator and cant figure it out

was observed over a certain period and the number 8. Neutrino radiation in which 0, 1, 2,.. signals were received was recorded. Number of Hours with This Frequency of Signals 1,924 541 Number of Signals per Hour 17 6 or more Test the hypothesis that the observations come from a population having a Poisson distribution with mean .3.

Answer 1

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

We used here MINITAB

first enter the data in MINITAB cells, in first cell enter number and second cell enter frequency.

now follow the following instructions:

Choose Stat > Basic Statistics > Goodness-of-Fit Test for Poisson.

In Variable, enter Number.

In Frequency, enter Frequency

Click OK.

Session window output

Goodness-of-Fit Test for Poisson Distribution

Data column: Number
Frequency column: frequency

Poisson mean for Number = 0.311944

                            
Number Observed Probability Expected       Contribution to Chi-Sq
0         1924      0.732022 1893.74         0.48347
1             541     0.228350      590.74            4.18840
2               103     0.035616    92.14        1.28018
>=3           19       0.004011   10.38       7.16525

   N DF   Chi-Sq      P-Value
2587      2 13.1173    0.001

Here we reject null hypothesis, Since p-value is less than 0.05

that is conclusion is Data does not follow the Poisson distribution. or does not come from Poisson distribution.