16 Statistics using random process Suppose telephone calls f

(16%) Statistics (using random process): Suppose telephone calls follow a Poisson process model X(t). There are two hypotheses on the expected value: H1: E[X(t)] = l₁t = 70t and H2: E[X(t)] = l₂t = 75t. We will use t = 30 in this question and suppose the number of calls received is 2175.

For a value a of significance level, there are four possibilities for accepting / rejecting the hypotheses: H1 and H2 both accepted, H1 and H2 both rejected, H1 accepted and H2 rejected, H2 accepted and H1 rejected.

Find / compute a significance level a (a = ?) that both H1 and H2 are accepted (show the calculation) or explain why such significance level does not exist.

Find / compute a significance level a that both H1 and H2 rejected (show the calculation) or explain why such significance level does not exist.

Find / compute a significance level a that H1 is accepted and H2 is rejected (show the calculation) or explain why such significance level does not exist.

Find / compute a significance level a that H2 is accepted and H1 is rejected (show the calculation) or explain why such significance level does not exist.

        (e) Repeat part (c) and part (d) of question 4 above assuming the number of calls received is 2150 instead of 2175.

Solution

chegg\'s policy allow me to answer only 4 sub parts so I would like to help with all your question but you need to post the final literal in other question

we need to know first the value for each H

for H1

2175/70= 31.07

for H2

2175/75=29

a)

significance level

we need to see what is the difference between t value and the values for each hypothesis

31.07-30 = 1.07

29-30 = -1 = abs(-1)= 1

1.07+1 = 2.07 / 100 =0.0207

significant level is 2.07%

b)

these significant level can be a lot of because only need to be major than 2.07% for reject both

c)

H1 accepted

we only need the value of H1 that is 1.07

significance level : 1.07%

d)

H2 accepted

we only need the value of H2 that is 1

significance level 1%