# 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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### Rao Score test and Neyman-Rao test

I've got the Laplace location/scale model where $X_1,...,X_n$ are iid random variables with common density \begin{equation} p_{\theta,\eta}(x)=\frac{1}{2\eta}e^{-|\frac{x-\theta}{\eta}|}. \end{...
1 vote
55 views

### Should I reject the null hypothesis or not?

EDIT: My apologies, I had a coding error. I accidentally used the same standard deviation for both samples. Now that I fixed that, both the normal and Student's confidence intervals are stupidly ...
1 vote
16 views

### Proof of statistical assumptions behind the methods or tests

When reading statistics literature, they provide the assumptions of when specific tests/methodologies can be used. Take factor analysis as an example; you may find this inside a paper: "Generally ...
14 views

### Minimum required sample size and confidence interval of the difference

I have calculated a minimum sample size required to compare difference between two independent proportions using various online sources e.g. this one or G*Power software. Here are the details: P1: 0....
21 views

### Is my answer to this Poisson distribution story problem correct?

Andreia's secretary makes random errors in his work at an average rate if 1.7 errors every 100 words. (a) Andreia offers the secretary a choice of one of two bonus schemes, based on a sample of 40 ...
21 views

### hypothetical test [closed]

Suppose that $X$ is a sample of size 1. Given a significance level $\alpha\le 0.1$, derive a UMP test of the following hypotheses $[H_0: X\sim N(0,1)\ vs.\ H_1: X\sim DE(1/2)]$, where $DE(\lambda)$ ...
18 views

### Testing the generation of a sequence of zeros and ones

I am given a sequence of $40$ ones and zeros, and I have to test whether the sequence is random (in the problem this is said to be equivalent to testing the null hypothesis that all ${40 \choose n_1}$ ...
33 views

### most powerful test of exponential distribution

It is assumed that X, the lifetime (in hours) of a light bulb, follows an exponential distribution with the following probability density function: f(x; λ) = 1/λ(e^-x/λ) if x > 0 or 0 otherwise (a) ...
1 vote
35 views

### hypothesis testing with central limit theorem

Company A claims that the average number of biscuits in a tin of BiskO shortbread biscuits is $27$. The fair business regulators believes that the Company A’s claims are inaccurate, and that the true ...
12 views

### Hypothesis testing for the probability of a graph being conected

Given the probability of every two nodes being connected, write a simulation to estimate the probability of a connected graph. Then use hypothesis testing to justify the result. I can write a Monte ...
32 views

### Determine c so hypothesis test has level of significance α= 0.05

I have the solution but can't find an explanation that makes sense to me so I'm hoping someone here can explain it to me. Question: Consider a sample with just one observation $X$ that is assumed to ...
1 vote
18 views

### UMP test-why is it wrong to check it this way?

So, I want to know if a test is a UMP test. for: $θ_0=3$ $θ_1<θ_0$ using neyman-pearson lemma suppose I got something like this where our estimator for $θ_0$ is the mean and for some ...
14 views

### How to test randomness of assigning the incoming call to the call center employees?

We have the call center with 6 employees in total. We can't predict when each of them will work, however we would like to ensure that the employees are chosen at random to pick up incoming calls. How ...
1 vote
29 views

### Hypothesis testing on sample mean when observation are correlated

How can I test whether the mean of a sample is significantly larger than the population mean, when observations are not independent, but the exact correlation matrix is known? I have a variable $X$ ...
1 vote
We have binary hypothesis testing problem as follows: $H_1$ (signal presence) : $y = s + n$ $H_0$ (signal absence) : $y = n$ Without loss of generality, to simplify the problem, let s be a constant ...