Question

A certain electric power company maintains that its average rate of critical home electrical power failures is 1.3 failures per day. From analyzes carried out in previous years, it is known that critical failures appear according to a Poisson process. The failure repair team in electrical networks of that company maintains that the failure rate received per day is higher and chooses to make a count of the number of failures reported to it during the month of May to prove it.
to.

a.If we assume that what the electric power company says is true:
i.What is the expected number of failures during the month of May?
ii. What is the probability that 41 failures or fewer will occur during that month?
b. Indicate what the hypothesis is and its denial.
c. Tell what the probability distribution of the statistic is if the hypothesis is assumed to be true.
d. If the team establishes the criterion that they will reject the hypothesis if the variable of interest (statistical) exceeds the mean by 1.8 standard deviations, it establishes:
i. What is the rejection criterion according to the value that the variable (statistic) takes in the month of May?
ii. What is the level of significance (type 1 error) with which the repair team would reject the hypothesis?

e.At the end of May, the count of failures reported to the repair team was made in the month and they found that there were 49.
i. How many standard deviations from the mean is the result obtained in the sample?
ii. What is the p-value of the result found?
f. Is the hypothesis rejected or accepted? Be specific in explaining why it is rejected or not rejected. Indicates the level of significance with which the hypothesis is rejected or not.
g. It concludes in the context of the problem.
[Answer: 40.3, 0.5848, X≥52, 0.0431, 1.37, 0.1008]

Answer 1

a)

i) If we assumen the claim of the electric power company to be true, the expected number of failures in the month of May is 1.3*(Number of days in the month of May) = 1.3*31 = 40.3 failures

ii)

Let X: Number of failures in May

Required probability = P(X <= 41)

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