# Hypothesis testing case

## Homework Statement

Given ##X_1,\dots,X_{100}##, test ##H_0: \lambda=1## against ##H_a: \lambda=4##. The mean ##\bar{X_{100}}=1.5##
(1) Take the decision on 3% level.
(2) Find the p-value

## Homework Equations

##t=\frac{\bar{x}-\mu}{s/\sqrt{n}}##

## The Attempt at a Solution

The level of significance is ##0.033##. The p-value I need to evaluate ##\frac{\bar{x}-\mu}{s/\sqrt{n}}##, but I am missing ##s##. Is it still possible to have a solution?

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Mentor
Is that the full problem statement?

Is the Poisson distribution mentioned somewhere?

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## Homework Statement

Given ##X_1,\dots,X_{100}##, test ##H_0: \lambda=1## against ##H_a: \lambda=4##. The mean ##\bar{X_{100}}=1.5##
(1) Take the decision on 3% level.
(2) Find the p-value

## Homework Equations

##t=\frac{\bar{x}-\mu}{s/\sqrt{n}}##

## The Attempt at a Solution

The level of significance is ##0.033##. The p-value I need to evaluate ##\frac{\bar{x}-\mu}{s/\sqrt{n}}##, but I am missing ##s##. Is it still possible to have a solution?
Do you mean that the upper limit on the type-I error is 3%? How did 3% become 0.033?

Are ##X_1, X_2, \ldots, X_{100}## independent and identically distributed? Are they Poisson random variables? If they are Poisson, you can use the formula for the variance of a Poisson to get the exact standard deviation ##\sigma##, so there is no need to use the unavailable sample variance, ##s##. (However, for a Poisson, variance is a function of the mean, so be careful).