# Questions tagged [hypothesis-testing]

This tag is used for questions regarding how to construct, use a hypothesis test or what is the appropriate test to use for a given case

920 questions
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### Assume the hypothesis $H_0 : u = 59$ by computing the relevant $p$-value

An observed sample of four observations from $N(u, \sigma^2)$ distribution has mean $54.75$ and standard deviation $10.21$. A table of quantiles of the chisquare distribution is given below $(a)$ ...
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### Exponential Test

Given a collection of data points, without any other information I want to test for an exponential distribution. In a different case, I tested for normality using an Accord implementation of the ...
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### Test if reduction of coefficient of variation is significant

I have the following problem: I want to compare two different quantification processes and I use the coefficient of variation as quality metric. So in principle my data look like: experiment method1 ...
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### Two population hypothesis test sample size

A retailer is trying a new concept in 3 of its 200 stores. The trial period is 10 weeks. The goal is to increse sales with at least 10%. The tricky part is that there is sesonality and campaigns that ...
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### Hypothesis testing variance using sample mean

I know how to test hypotheses for variance using methods like the chi-square test. However, this problem is asking me to use a rejection region construction in terms of the sum of the sample values (...
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### Hypothesis testing for sample means within a normal distrubution

The context of the question is that a bakery bakes cakes and the mass of cake is demoted by $X$ such that $X \sim N(300, 40^2)$. A sample of 12 cakes is taken and the mean of the sample is 292g. The ...
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### Getting a probability $> 1$ in hypothesis test

I have the following hypothesis question. A soft drinks company claims that of all consumers buying their product, $82 \%$ prefer the light version of the drink. To test their claim, data were ...
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### Hypothesis test concerning a population proportion

The problem states that the national on-time arrival rate for flights in Nov 2018 is 79.66% according to the Bureau of Transportation. Suppose in Nov 2018, we ...
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### Testing if cross-covariance is zero in Hilbert spaces

I'm attempting to generalize a multivariate test of zero cross-covariance between two random varaibles to infinite dimensional Hilbert spaces and I'm looking for some advice / ideas on how to work ...
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### wilcoxon signed rank test interpretation

I try to understand the Wilcoxon signed rank test, but I have not been profoundly successful. I have studied various articles and educational videos, but I have not succeeded yet. The concept I'm ...
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### Hypothesis Testing under Uniform Distribution Question

The question reads: Let $\theta > 0$ and $X \sim \mathcal{U}[0, \theta]$, i.e. $X$ is uniformly distributed on the interval $[0, \theta]$. Assume that $\theta$ is unknown, but we can observe $X$. ...
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### Interpretation of the p-value and the test-statistic W of the Shapiro.test in R

Shapiro-Wilk normality test data: Part1 W = 0.14846, p-value = 6.478e-16 Shapiro-Wilk normality test data: Part2 W = 0.47978, p-value < 2.2e-16 Shapiro-Wilk normality test data: Part3 ...
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### Testing cross-covariance in the residuals of a VAR(p) model

Suppose I have a vector autoregressive model of order $p$: $$y_t = c + A_1 y_{t-1} + ... + A_p y_{t-p} + u_t$$, where $y_t$ is a $K\times 1$ vector and $A_i$ are $K\times K$ matrices. We assume the ...
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### How do I test if an observed point is expected from a linear regression?

I have a set of $N$ observations on $x$ and $y$, where each observation is characterized as a couple of Gaussian distributions $x\sim N(x_i, {\epsilon_{x,i}}^2), y\sim N(y_i, {\epsilon_{y,i}}^2)$, ...
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### Changing the null hypothesis in a t-test

Hello. I am working on a problem and am confused. What I know so far is that the two-sided t-test with $\alpha=.05$ will reject the null since the $p-$value is smaller. Here is where I am lost. The ...
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### Calculate confidence-level in A/B-test on revenue

I'm doing a split-test and need to calculate the confidence-level of the result. I need to implement the calculations on my own, not using any online-tools or excel. I managed to do this for binomial ...
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### Can the Central Limit Theorem be applied here?

My problem statement is to identify in a healthcare organisation, which of it's doctors are lagging in providing proper care to their patients. My Random Variable X is defined as {0 if the patient ...
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