5. It is believed that when a certain type of uranium is placed in a radioactive counter for a given interval of time, the number X of gamma particles emitted during the interval behaves as a random variable having the Poisson distribution. In an experiment, the number of emissions from a piece of uranium was obtained for each of 50 intervals of equal length with the results shown below. Use the chi-square goodness-of-fit test to test the null hypothesis at the 5% level of significance that the data behave like a sample from a Poisson population.

Number of gamma particles 0 1 2 3 4 5 6 Observed time intervals 2 3 10 12 14 5 4