How Do You Test a Hypothesis Without Sample Variance?

[GabrielN00]

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?

 

[mfb]

Is that the full problem statement?

Is the Poisson distribution mentioned somewhere?

 

[Ray Vickson]

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).