Statistics confidence coefficient calculation

In summary, to find a significance level α for accepting both Hypothesis 1 and Hypothesis 2, we need to calculate the p-values for each hypothesis using the given values of λ and t. Then, we can take the minimum value of the p-values and use it to compute α using the equation α = P( (u - E[Y] / stdY > c / stdY). However, further steps are needed to determine the exact value of α.
  • #1
cutesteph
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Homework Statement


Suppose you receive calls that follow a Poisson process model Y(t).
There are two hypotheses, Hypothesis1: E[Y(t)] = λ1t = 71t and Hypothesis 2: E[Y(t)] = λ2t = 74t. Let t = 30 the number of calls be 2175.

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

Homework Equations



α = P( (u - E[Y] /stdY > c / stdY)

The Attempt at a Solution



hypothesis 1: u= 71 std = sqrt(71)

hypothesis 2: u = 74 std = sqrt(74)

Am I suppose to take the minimum value of the p values of each?
 
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  • #2
p1 = P( (2175 - 71t) / sqrt(71t) > c / sqrt(71t)) p2 = P( (2175 - 74t) / sqrt(74t) > c / sqrt(74t)) I am not sure how to proceed.
 

What is a confidence coefficient?

A confidence coefficient is a statistical measure that represents the level of confidence that a researcher has in their findings. It is typically expressed as a percentage and represents the probability that the true value falls within a certain range of the estimated value.

How is the confidence coefficient calculated?

The confidence coefficient is calculated using a formula that takes into account the sample size, the level of confidence desired, and the standard deviation of the sample. This formula varies depending on the statistical test being used, but it typically involves multiplying a critical value (obtained from a statistical table) by the standard error of the estimate.

What is the relationship between confidence coefficient and confidence interval?

The confidence coefficient and confidence interval are closely related. The confidence interval is the range of values within which the true value is likely to fall, while the confidence coefficient is the likelihood that the true value falls within that range. A higher confidence coefficient indicates a narrower confidence interval, meaning that the researcher is more confident in their findings.

What is a common confidence coefficient used in statistical analysis?

A common confidence coefficient used in statistical analysis is 95%. This means that there is a 95% probability that the true value falls within the estimated range. This is also known as a 95% confidence interval.

Why is it important to calculate the confidence coefficient?

Calculating the confidence coefficient is important because it allows researchers to determine the level of confidence they have in their findings. This helps them make informed decisions and draw accurate conclusions based on their data. It also allows for comparison between different studies and helps to determine the reliability of the results.

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