# How Do You Test a Hypothesis Without Sample Variance?

• GabrielN00
If they are not Poisson, then you would need to make some assumptions about the distribution to get an estimate of ##s##.
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?

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Is that the full problem statement?

Is the Poisson distribution mentioned somewhere?

GabrielN00 said:

## 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).

## 1. What is the purpose of hypothesis testing in a scientific study?

Hypothesis testing is used to determine the validity of a proposed hypothesis or research question by collecting and analyzing data. It allows scientists to make conclusions about their theories and determine whether they are supported by the evidence.

## 2. How do you choose the appropriate statistical test for hypothesis testing?

The appropriate statistical test for hypothesis testing depends on the research question, the type of data collected, and the number of variables involved. Generally, the choice of statistical test is determined by the type of data (e.g. categorical or continuous) and the number of groups being compared.

## 3. What is the difference between a null hypothesis and an alternative hypothesis?

A null hypothesis is a statement that assumes there is no significant difference between two or more groups or variables. An alternative hypothesis, on the other hand, suggests that there is a significant difference or relationship between the groups or variables being studied.

## 4. What is the significance level in hypothesis testing?

The significance level, also known as alpha (α), is the predetermined level of probability that is used to determine whether the results of a study are statistically significant. Typically, a significance level of 0.05 (or 5%) is used, meaning there is a 5% chance that the results are due to chance rather than a true difference or relationship.

## 5. Can hypothesis testing prove causation?

No, hypothesis testing cannot prove causation. It can only determine the likelihood of a relationship between variables, but it cannot establish a cause-and-effect relationship. Other factors and variables that were not considered in the study could also be responsible for the observed results.

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