# Questions tagged [hypothesis-testing]

This tag is for questions on hypothesis testing in statistics, including questions about constructing or setting up a test, selecting an appropriate test for a particular application, and computing test statistics.

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### Statistics: Hypothesis testing to find p-value [migrated]

I am currently writing a thesis in machine learning and I am trying to use t-test to show that my model is better than the current state of the art. The dataset I used has 16 different tasks and each ...
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### Using hypothesis testing to check if a mean of a sample is bigger than the other sample.

Basically I am asked if people over age $35$ spend more money on average than people less or equal to age $35$ with significane level $0.05$. And I have a sample of the population that I can use for ...
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### generic constant and Student d.f.

What is a generic constant $k$ in the context of significance of the correlation coefficient ? Please see $(11.4.10)$ the snippet below:
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### Chi-square GoF test

Joe likes coin tricks. In one of his tricks, he flips a coin $3$ times. Let $X$ be the number of heads that appear. Joe will repeat this trick so that we have $n$ samples from $X$. Although Joe doesn'...
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### Hypothesis testing and critical regions

Suppose $X$ follows a chi-squared distribution with $r$ degrees of freedom, where $r \in \mathbb{Z}^+$ is unknown. Let $X_1, X_2, ..., X_n$ be a random sample of $X$. (i) Suppose we have the following ...
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### Hypothesis tests two means

For a random person selected from a population, let $X$ be their Instagram followers and $Y$ be their Facebook followers. We randomly sample the followers of $n$ people, $(X_1, Y_1), ..., (X_n, Y_n)$. ...
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### Testing hypotheses proportions

John is an avid soccer player. Last season, he scored a goal $50$ times out of $200$ attempted shots. This season, he will have $200$ attempts. (i) Using John's previous statistics, determine the ...
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### Calculating the p value for the sign test

I am utterly confused at calculating the p value for both single sampled and matched pair sign tests. Suppose we have a sample size of 12 and 4 values are below our hypothesized median of $m_x$ and 8 ...
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### How to check if a distribution follows a power law?

I have a distribution of the node degrees to their fraction (%) in a network, which may contain 10 to 100 values, all between 1 (max) and near zero. I would like to see if it follows the Power law ...
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### Critical value: Testing two normal samples for equality of population variances. [closed]

To test the hypothesis that two population variances are equal, a random sample of size 13 was selected from the first population, and a random sample of size 21 was selected from the second ...
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### Hypothesis testing for proportions from three populations

I have following problem : 200 people were surveyed asking about their favorite color. 80 of them said red, 85 blue and 35 said yellow. Verify following hypothesis : proportion of people liking red, ...
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### The semantics of rejecting the null hypothesis

My professor said that "You should never accept the null hypothesis, instead you state there is insufficient evidence to reject the null hypothesis" and that led me to a loophole of ...
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### Need for equality in the null hypothesis

In statistical hypothesis testing, the alternate hypothesis is usually chosen to be the statement which bears the burden of proof. Also, the null hypothesis always has an equality ($\leq$ or $\geq$ ...
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### Statistical test to prove equivalence of two classifiers

I am trying to empirically show equivalence between a logistic regression classifier and another classifier based on a maximum entropy argument. What I have done is used both classifiers on the same ...
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### Hypothesis testing for a Poisson distribution

Let $\mathbf{X}=\left\{X_{1}, X_{2}, \ldots, X_{n}\right\}$ be an independent random sample from the Poisson distribution with parameter $\theta>0$. (i) Find the rejection region of the most ...
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### “Invariance” of Pearson's Chi-squared test

A company has 100 employees, 40 women and 60 men. At the end of the year, the company decides to give bonuses to 20 people: 16 men and 4 women. I'm asked to find a way to test the presence of a ...
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### Sample size formula for linear mixed effects model

I am looking for a sample size formula for a linear mixed effects model to achieve a certain power. I am familiar with the derivation that assumes a two stage formulation, where stage 1 fits the ...
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### hypothesis testing and CI

when can't we test the hypothesis testing based on confidence interval and when can we? I just know that one example is since we have used estimator of p to estimate the normal distribution but we use ...
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### 1 Mean T-Test, Statistics

During a flu vaccine shortage in the United States, it was believed that 45 percent of vaccine-eligible people received flu vaccine. The results of a survey given to a random sample of 2,350 vaccine-...
2answers
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### Significance Hypothesis Testing

Given an assumed mean of 60, a standard deviation of 6, and a population with a sample size of 50 and a population mean of 62.6, I was able to set up two hypotheses, H0, $\mu=60$ H1, $\mu \ne 60$ I ...
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### Why do I have to use a fear as the Alternative-Hypothesis?

Introduction I'd like to understand, why I have to use a fear as the Alternative-Hypothesis and not as the Null-Hypothesis. I'm using my homework as an example for that, which says the following (I ...
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### Hypothesis testing - critical region

When finding the critical region, do you choose the x values closest to the significance level even if its bigger then it or does the value have to be smaller then the significance level. So if a ...
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### Fisher's exact test calculation

I want to determine whether a new technique for sampling blood cultures causes less contamination of the blood cultures. The group in which i applied the new technique is called the intervention group ...
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### How can I determine statistically how well my estimator predicts actual results?

I have a business in which I contract with my clients to perform work for them for an indefinite amount of time. To forecast my profitability, I need to forecast when my existing contracts will end. ...
2answers
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### Most powerful test. Help using Neyman Pearson

$X_1,X_2,...$ independent continuous random variables with p.d.f $f(x) = \theta x^{\theta-1}$ if $0<x<1 , 0$ otherwise for $\theta > 0$ sample size = 1 Use Neyman-Pearson Lemma to drive MP ...
1answer
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### statistical hypothesis testing.

Vasya Sidorov claims that he goes to the cinema twice as often as to the gym, and to the gym twice as often as to the theater. Over the past six months, he has been to the theater 10 times, to the gym ...