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

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Discussion Overview

The discussion revolves around a homework problem involving a Poisson process model with two competing hypotheses regarding the expected number of calls. Participants explore how to compute a significance level that would allow for the acceptance of both hypotheses at a confidence level of 68%.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents a homework statement involving two hypotheses about the expected number of calls in a Poisson process.
  • Another participant inquires about the approach taken to solve the problem, suggesting familiarity with confidence intervals and the Poisson distribution.
  • A participant mentions using a normal approximation for the Poisson distribution due to a large sample size and notes that the variance of a Poisson distribution equals its expected value.
  • There is a question posed about whether both hypotheses can be accepted at a 68% confidence level.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants exploring different approaches and considerations without reaching a consensus on the acceptance of both hypotheses.

Contextual Notes

Participants have not fully detailed their assumptions regarding the significance level or the specific methods for testing the hypotheses, leaving some steps and definitions unclear.

cutesteph
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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
 
Last edited:
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Good question - how are you attempting the problem?
Presumably you've done problems involving confidence intervals and/or poisson distributon before?
 
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?
 
Last edited:
Well to 68% confidence limits, would you accept both hypotheses?
 

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