# 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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### What is the null hypothesis?

A person claims that he can differentiate if a medicine is working or a placebo. Therefore we test the null hypothesis $p=0.5$ and $\alpha=0.5$ with $n=50$ with a right handed hypothesis test. Edit: ...
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### Hypothesis testing for anti proportional correlation

currently I am a bit in trouble regarding hypothesis testing - definitely my weakest area of math. I was studying it quite a lot in the past days but came across an problem that I don't know how to ...
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### Is my Z-Test incorrect? [closed]

Wondering if I could have a second pair of eyes peer review my Z test that I have recently conducted, Hypothesis H0: u1 = u2 H1: u1 > u2 Calculations performed in the image attached: Z-Test ...
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### The value of threshold for Hypothesis testing

Is the threshold in Hypothesis testing (I mean the value that we compare the test output with) always between zero and one? and Why? Any help will be much appreciated.
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### Transformation to remove column in regression proof

I'm trying to show that the $F$ statistic where the smaller model is just the removal of the $j$th predictor is equivalent to the square of the $t$ statistic for question $3.1$ in Elements of ...
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### Power of point hypothesis test

With $X_i$ i.i.d. $N(\theta,1)$ and $$H_0: \theta=0 vs. H_1: \theta=1$$ I got that the test statistic is $\bar{X_n} > \frac{q_{\alpha}}{\sqrt{n}}+\theta$, where $\theta$ is either 0 for $H_0$ or 1 ...
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### Why is hypothesis testing used at all?

I've been reading about different criticisms about the misuse of p values adn hypothesis testing in different fields and I think I understand the main issues with how people wrongly interpret them. In ...
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### obtaining the t_P value of the partial correlations

sorry if this sounds stupid, the following picture is from a paper I am reading, I have obtained a matrix of r (the partial correlations of each predictor with the response variable) and I have the ...
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### Find the test that minimizes the sum of the type 1 and type 2 error probabilities [closed]

Let we had one observation of $X~ N(\mu,1)$ And consider test : $H_0:\mu=0, H_1:\mu=1$. How to find test that minimizes sum of probablities of type 1 and type 2 errors?
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### Test hypotheses using statistic value

I have an exam today, and the solution to this problem that my teacher provided differs from mine: A government department estimates that at most the 12% of the people older than 65 years has a ...
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### Critical region for testing a hypothesis with exponential data.

I have trouble with the following problem: We assume that X has a Exp(λ)-distribution with a unknowns value of λ. We test H0: λ=0.2 versus H1: λ < 0.2. We use X as test statistic. a. ...
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### Hypothesis testing with a exponential distribution

I have the following problem: Given the data $X_1, X_2, \ldots, X_{15}$ which we consider as a sample from a distribution with a probability density of $\exp(-(x-\theta))$ for $x\ge\theta$. ...
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### Statistics: finding an MLE for theta

I have to obtain a likelihood-ratio test for $H_0: \theta =0$ vs $H_1:\theta \neq 0$. $\theta \in [-1,1]$ I also think the size of the random sample is $n=1$, it says "given an observation of $X$". ...
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### Is a 99% confidence level more precise than 95%?

Hi. I'm confused by 'significance level'. If significance level is lower, is the result of test more reliable? I think it's the opposite, so it makes me so confused. Look at the picture and assume ...
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### Failed Uniformly Most Powerful Test

Suppose $X_1,...,X_n$ is a random sample from $N(\theta,1)$. We want to test $H_0: \theta = \theta'$ vs $H_1: \theta \ne \theta'$. I know that since there are 2 critical region for $H_1$, there is no ...
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### Creating a confidence interval when sigma is unknown

This is something which has plagued me for months now. And i am not really able to explain it to anyone. I know how to CALCULATE the confidence interval when sigma is unknown . But i don't get how is ...
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### Show that a critical region $G$ based on the likelihood ratio is of the form $G=B_{R_1}\cup\overline{B_{R_2}^c}$

From an $N(0,\sigma^2)$- distributed population one draws a sample $X_1,...,X_n$ of size $n$ in order to test the hypothesis $H_0: \sigma=1$ against $H_1:\sigma \neq 1$. Let $B_R$ be the closed ball ...
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### Estimation of the Kolmogorov test power [Rstudio].

Let $x$ be a 20-element sample from the T-Student distribution with 4 degree of freedom. I want to do a simulation to estimate the power of the Kolmogorov test for $H_0=F\sim N(0,1)$ if $\alpha=0.01$. ...
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### Is my six sided dice weighted?

I was playing a game with my son, and it seemed that we rolled two or five about half the time. He was wondering if the die was weighted. So I re-rolled it a bunch of times and jotted down the ...
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### LRT statistic on data

I have a dataset with variables date sold, prices, type (house/unit) and number of bedrooms. I have fitted the data with weibull distribution on the variable 'prices' with fitdist(). I would like to ...
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### Is there a proper scoring rule on a general topological space $X$?

I have seen (proper) scoring rules on binary, multiple-choice, and real-valued questions, such as Brier Scores, log scores, and a few others for real-valued examples. Is there any literature on ...
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### NP Lemma and rejection region having the size.

quick question. I need to find the rejection region of H_0, meaning that I need to find the constant value for which if X=x belongs to the region H_0 is rejected. The pdf is c(1-x)^(c-1) with x ...
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### Check for distribution of the sample with unknown parameters using ks.test in R.

When I do a ks.test in R for a sample to check from which distribution it is, it gives me a $p$ value less than 0.01 for various distributions and I don't know why. Maybe because of parameters or smth?...
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### Minimizing Type I and Type II errors Simultaneously

I am trying to understand why I can't simultaneously minimize Type I error and Type II error simultaneously. A non-randomized Hypothesis test is essentially a deterministic partition of the Range ...
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### A machine is used to fill packets with rice. The contents of each packet weighs X grams - Normal Distribution

A machine is used to fill packets with rice. The contents of each packet weighs X grams. X is normally distributed with mean μ grams and standard deviation 3.71 grams. The mean weight μ is stated to ...
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### Hypothesis testing for the variance of a population

Someone is trying to introduce a new process in the production of a precision instrument for industrial use. The new process keeps the average weight but hopes to reduce the variability, which ...
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### A research department is investigating the duration of a tire.The department wants to show it exceeds a certain value. Formulate the hypothesis

The research department of a tire manufacturer is investigating the duration of a tire using a new rubber component. 16 tires were produced and the duration was tested. The average duration and ...
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### how to calculate the Wald test statistic

I am struggling to understand the definition as I am seeing several different definitions on the internet. Lets say I have a question that goes like : Given $Y_1 ...Y_n$ is a sample taken from ...
Using Neyman Pearson Lemma, find a Most Powerful test for $H_0 : \sigma = 2$ vs. $H_1 : \sigma = 1 \$ at level $\alpha$ based on a random sample $X_1, \dots , X_n \$ from $N(3, \sigma^2 )$. Also ...
Suppose X has distribution in $\mathcal{P}=\{B(10, \frac{1}{2}), P(1)\}$ (Binomial and Poisson respectively). Let $H_0 := X \stackrel{D}{=} B(10, \frac{1}{2})$ and $H_1 := X \stackrel{D}{=}P(1)$. ...