I am having problems solving this problem of statistical inference and I do not know if it is well done or not, so I would like someone to review it. I just started with inference, so I have my problems.
-The weekly number of failures due to software problems that have occurred in a computer system are the following:
Number fails 0 1 2 3 4 5 6 8 Frequency 41 62 63 38 12 7 1 1
1) Can it be accepted that the weekly number of failures due to software problems that occur in that computer system is a random variable with Poisson distribution?
What I have to do is calculate the chi-square, which I get from Chi-Square values = 379,682 with 11 g.l. Value-P = 0,0 It does not fit me since it gives me a p-value of 0 and it never happened to me, so I do not know if you could tell me that this result is true
2) Assuming that the weekly number of failures due to software problems is distributed according to a law Poisson: Calculate an unbiased estimate of the weekly rate of system failures due to software problems.
What I have to calculate is a mean that the best estimator (and also unbiased is the sample mean) that has a value of 1.77333 to be unbiased E (Estimation) = μ and because E (Average) = μ We concluded that he would be unbiased.
3) Calculate a level confidence interval of at least 0.94 for the distribution parameter.
I have this, but I am not very confident that it is correct:
Average (x): 1,77333 Standard deviation (s): 1.36185 (x +/- Ks) 100 (1-1 / K ^ 2) = 94; K = 4.0824 1.7733 +/- 4.0824 * 1.36185 = [-3.7863, 7,3329]
4) Calculate a confidence interval of approximate level 0.94 for the distribution parameter using the central limit theorem.
Of the sample rate I have my own mean which is 1.7733 and of null hypothesis, as they do not tell me anything, I suppose 0.5 for n = 225 and I get the IC [1.61016, 1.94868]
5) Can it be accepted, at a level of 2%, that, as the engineer responsible for the system says, the weekly failure rate is at most 1.6? And at a level of 5%?
It is the same exercise as the previous one but with a null hypothesis of 1.6, for an average of 1.7733 and n = 225. As it tells me that it is unilateral less than (HERE I HAVE DOUBTS IF IT IS UNILATERAL LESS THAN) and with the p-value of 0.981321 I conclude that I can not reject the null hypothesis for alpha 0.02.
For 5% I get the same p-value and same conclusion of rejection