Can Both Hypotheses be Accepted with a Confidence Level of 68%?

[cutesteph]

1. Homework Statement
Suppose you receive calls that follow a Poisson process model Y(t).
There are two hypotheses, Hypothesis1: E[Y(t)] = λ1t = 70t and Hypothesis 2: E[Y(t)] = λ2t = 75t. Let t = 30 the number of calls be 2175.

Find and compute a significance level α such that both Hypothesis1 and Hypothesis2 are accepted.
2. Homework Equations

α = P( (u - E[Y] /stdY > c / stdY) 3. The Attempt at a Solution

 

[Simon Bridge]

Good question - how are you attempting the problem?
Presumably you've done problems involving confidence intervals and/or poisson distributon before?

 

[cutesteph]

Opps, I forgot to type my approach. Since n is big, we can approximate the poisson with the normal.
The variance of a poisson is the same as the expected value.
Or am I suppose to use a two sided test?

 

[Simon Bridge]

Well to 68% confidence limits, would you accept both hypotheses?