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.
1,616
questions
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Model of three mutually exclusive events to be accepted or rejected with confidence .05
According to a genetic model, three mutually exclusive characteristics A, B, C are present with probabilities:
P(A) = 0.1, P(B) = 0.2, P(C) = 0.7
In a random sample of size 100, A happens to appear ...
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2
answers
57
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Selecting a proper p-value (Chi-squared)
When studying about Chi-squared test and distribution, it's quite common to read that most people use p value equal to 0.05 or 0.01.
Do you have more information about what p values are good for ...
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177
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Show there is no UMP test for $N(\mu,\sigma^2)$
Here's a testing problem.
$X_1, \cdots, X_n, indep, \sim N(\mu, \sigma^2)$ where $\mu, \sigma^2$ are unknown.
$H_0: \mu \le \mu_0$ vs $H_1: \mu > \mu_0$ where $\mu_0$ is specified.
I need to ...
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1
answer
927
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Hypothesis testing: Test statistic, P-value and significance levels
A manufacturer claims his light bulbs have a mean life $μ = 1800$ hours. A consumer group tested a random sample of $n = 250$ bulbs and found them to have a sample mean life $\bar{x} = 1790$ hours ...
1
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1
answer
263
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Shapiro-Wilk test
I am trying to determine if a given sample comes from a Normal distribution. For that purpose I want to perform a Shapiro-Wilk test in the way stated on wikipedia. My concern comes with the vector $(...
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1
answer
538
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two sample t-test not matching R
I'm trying to do a hypothesis test and I've been told that my alternative hypothesis is that male students are older on average than female students in this particular survey.
I've set it up as ...
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1
answer
442
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How to calculate the HHG (Heller Heller Gorfine) correlation
HHG (A consistent multivariate test of association based on ranks of distances) is introduced in:
Heller, R., Heller, Y., & Gorfine, M. (2012b). A consistent multivariate test of association ...
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47
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relation between two gaussian vectors.
suppose I have two vector of unequal length, $X =\left \{ x_1, x_2, ... x_n \right \}$ and $Y =\left \{ y_1, y_2, ... y_m \right \}$ . Each element follows the same gaussian distribution , ...
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1
answer
35
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Lack of 0 in a 2-sample confidence interval
A problem asked me to explain why a $99\%$ confidence interval of the difference of two sample means did not offer substantial evidence of a difference in the two populations. The interval was ...
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1
answer
45
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Statistcs Wage Problem
I need some help on how to solve this question, what approach or rules to use? Im not really sure. Do I need to use hypothesis testing?
A company director took a sample of salaries of 13 employees ...
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3
answers
168
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Hypothesis Testing, paired mean
I am kind of stuck on this question, I don't really know how to approach it and I would appreciate some help.
The number of crime incidents during a period of 10 years were recorded in a certain ...
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1
answer
406
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What statistical test should i use for the given scenario?
I have an hypothesis that in people who have used both ios and android, a majority of them say 70% prefer android. I have a sample size of 50-60 users who have used both ios and android. What ...
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1
answer
172
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Question related to chi-square test of independence and likelihood ratio test
I'm solving a question regarding the independence of two criteria and I already found the right value for the likelihood ratio test (which in this case is 0.482, by summing 21 $ln$ (0.21) + ... + 14 $...
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1
answer
588
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Likelihood ratio critical region
Let $X_{1},..,X_{n}$ be a random sample from a normal distribution with mean ${\theta}$ and variance 1. We wish to test $H_{0}:{\theta}=0$ vs $H_{1}:{\theta}{\neq}0$. Write down likelihood ratio ...
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162
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Choosing which hypothesis test to use?
I'm sitting a statistics exam this week, and I'm having trouble recognising which test to use?
We get told either
a) use a parametric test or
b) use a non-parametric test
but is there a method to ...
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0
answers
14
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Algorithm to exclude false positives
I want to do the following: For a list of some hundreds participiants where some measure belongs to each participant, I want an algorithm that determines at which sample size a t-test or such would ...
2
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0
answers
51
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How to test a hypothesis which compares set of pairs of statements?
I've conducted an experiment but I'm not sure how to proceed with statistical analysis of it.
I have pairs of sentences created by two groups of people A and B, semantically the sentences in each ...
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0
answers
34
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Fast uniformity test within a ball.
Assume I have a dataset lies within a ball centered around the origin, I want to test the uniformity of the point distributed in the ball. In addition, I have all the distances to the origin computed ...
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1
answer
56
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hypotheses test when given two populations
I have the following data on duration that different aged adults can remain standing.
...
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1
answer
24
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Who do the Expected Values have this bound
Let $E_i$ be the expected frequency and $O_i$ the observed frequency.
For example, if we role a six-sided die $120$ times then $E_i = 20$ for all $1 \le i \le 6$, while the $O_i$ will be however ...
10
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1
answer
6k
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What is a $\it{nontrivial}\,$ Square Root?
I need to understand the concept behind a non trivial square root. Also how to answer these two questions and how to get to the answer?
Give a non-trivial square root of 30
Give a non-trivial square ...
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1
answer
1k
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An Application of the Neyman-Pearson Lemma.
Problem: Using the Neyman-Pearson Lemma, determine the most powerful test of size $ 5 \% $.
I know the Neyman-Pearson Lemma says that the test with the critical region
$$
\left\{
x \in \{ 1,2,3,4 \} ~...
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1
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62
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Determining hypothesis test and application
I'm running into issues trying to figure out what type of test to use and whether two tailed or one tailed in different scenarios. How do you determine what to do in the scenarios presented? For ...
2
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1
answer
585
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Testing hypothesis using significance levels
A random sample of n=26 observations on escape time (sec) for oil workers in a test resulted in sample mean 370.69 and sample standard deviation 24.36. Suppose the investigators had believed a priori ...
2
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1
answer
4k
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Power Function for the uniform distribution
Completely stuck on this homework question, I think my knowledge of the power function is nowhere near good enough coming up to finals!
Consider the following alternative testing problem: the
two ...
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1
answer
272
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Hypothesis testing on minimum of exponentially distributed random variables
I am completely stuck with the following problem, because I do not know how to start:
Let $X_1,...,X_n$ be independent and exponentially distributed with unknown parameter , and let $Y=min(X_1,...,...
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0
answers
45
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Why is $1 - \operatorname{P}(\text{Type I error}) =\overline{\operatorname{P}(\text{Type II error})}$?
I understand that in hypothesis testing, an increase in $\operatorname{P}(\text{Type I error})$ will lead to a decrease in $\operatorname{P}(\text{Type II error})$. However, why does an addition of ...
0
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0
answers
61
views
Which hypothesis test to use
Two identical machines are used to make a special coin. We want to know if they have the same variability. A random sample is taken from each machine :
$$ \begin{matrix}
MachineA & 135 & ...
0
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1
answer
684
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how to test a hypothesis when given population mean and standard deviation is known?
the mean weight of a 6 year old child is 49.3 lbs. another study indicated that in a sample of 196 six year olds the mean weight was 51.5 lbs. Assume a population standard deviation of 14. use the ...
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1
answer
1k
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Deriving most powerful test for hypothesis
Here is the problem I am studying:
"Consider a distribution with pdf $f(x;\theta)=\theta x^{\theta-1}$ if $0<x<1$ and
$0$ otherwise. Derive the most powerful test for the hypotheses of $H_0: \...
0
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1
answer
72
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Hypothesis testing using chi-square distribbution
Four players meet weekly and play eight hands of cards. Over a year, one of the payers finds that he has won x of the eight hands with frequency fx given in the following table:
x 0 1 2 3 4 5 6 7 8
...
1
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1
answer
457
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Neyman Pearson Lemma Question
I have the following question about the Neyman Pearson Lemma. It is an example in my lecture notes of testing $H_0:\theta=\theta_0$ against $H_1:\theta=\theta_1$ for the exponential distribution.
...
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1
answer
6k
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Upper and Lower Bounds for Confidence Intervals on a one tail hypothesis test.
CI(99) = xbar ± Zcv( σ / √ n -1 )
My question is if the test is a one tail hypothesis test, do I still do two separate equations + and -.
Here is the formula filled in (if it is the correct formula)...
0
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1
answer
71
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Hypothesis testing Type 1/2 error
If a test is done with a 95% confidence interval, what would be the percentage of Type 1 error? could you explain the theory behind the answer as well that would be appreciated.
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1
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31
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Test for Validity of Artificial Samples
I have a model that actually is learned from some observed samples. Then I use the model to generate several artificial data.
My question is: Which test should I use to test if the data is of the ...
0
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1
answer
155
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Finding p-value when df and test stat is given. PLEASE HELP. [closed]
For a chi-square goodness of fit test with 10 degrees of freedom, the test stat is 20.000, then how to find the p-value? In other words, what is ?: X^2?,10 = 20.000?
The X^2 table does not give the ...
0
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1
answer
69
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hypothesis testing two sample problem and standard error of mean
In my homework, I was asked to find the standard error of mean for 2 cases and then do the 5% and 1% test for both of them.
I know how to work out stand error of mean, but I don't know how to use it ...
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1
answer
367
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Real life scenario, probability model required for accidental vs supernatural causation.
A = HUMAN 1
B = HUMAN 2
A is related to B, specifically A is the father of B
A goes on holiday 5 years ago, staying in a hotel in popular tourist spot near Scotland (long way from home)
During ...
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2
answers
64
views
Difficulty to find the Standard Error in a simple hypothesis testing
I'm having some difficulty to solve a very simple hypothesis testing problem.
$$\begin{array}{c|c|c|}
& \text{X} & \text{Y} \\ \hline
\text{1} & 1 & 1 \\ \hline
\text{2} & 3 &...
1
vote
1
answer
490
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Hypothesis testing question
The article “Statistical evidence of discrimination” (J. Ameri. Stat. Assoc., 1982,
773-83) discussed the court case of Swain v Alabama (1965), in which it was alleged
that there was discrimination ...
1
vote
0
answers
19
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how to calculate p value of 2 sample
James and Margaret grow watermelons. Margaret claims her watermelons are heavier than James's watermelons. $40$ sample has been taken from both.
James: mean $7.3$ variance $0.4$
Margaret mean $11.3$ ...
0
votes
1
answer
106
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Allocating observations to test whether two expected values are equal$\mu_{1}-\mu_{2}=\Delta\neq 0?$
Question:
Suppose that you wish to test the hypothesis $H_{0}:\mu_{1}=\mu_{2}$ versus $H_{1}:\mu_{1}\neq \mu_{2}$,where both variances $\sigma^2_{1}$ and $\sigma^2_{2}$ are know ,A tatal of $n_{1}+...
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3k
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Solving problem with negative tcalc value. Please help.
Using the above data check to see if the average cholesterol determination was statistically the same or not for two labs. alpha= 0.05. Use a independent design.
My problem is that I got negative ...
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0
answers
246
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Testing hypothesis - type I and type II error
I have given following information:
$n=15$ - sample size
$S_n=0.013$ - sample standard deviation
I have to test null hypothesis $H_0(\sigma=0.01)$ agaist alternative hypothesis $H_1(\sigma>0.01)$...
1
vote
2
answers
1k
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Hypothesis test (when to use z-test or t-test)
I've got 6 questions here. I don't really need the complete answers, I just want to know what test (z or t) should be used and what are the basis for using that test. Here we go:
(1) According to the ...
4
votes
1
answer
1k
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Correlation Coefficient Distribution Function: An Apparent Discrepancy?
I'd like to explain an apparent discrepancy between:
(1) The sample correlation distribution function between sample vectors for a bivariate, correlated random variable (correlation coefficient = $\...
2
votes
1
answer
6k
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Why isn't a t test used when comparing two proportions?
All the examples I've seen say to use a z test to compare two proportions. For example, n=13, x=0.22 versus n=10, x=0.44. Then all the examples warn that the z test doesn't work with low sample sizes.
...
2
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1
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83
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Disagreement about rejection region for upper-tailed hypothesis test
If we look at the solutions for the first problem here and the first problem here, we see both problems are one-tailed tests for the upper-tail. However, in the first paper the rejection region is Z > ...
2
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2
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1k
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Building intuition of hypothesis testing
I'm studying AS level mathematics ("college") as a mature student and trying to wrap my head around binomial probability and hypothesis testing.
I understand that $X\sim B(n,p)$ describes a binomial ...
1
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1
answer
97
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Pairwise wilcoxon-mann-whitney?
Is there something like a pairwise version of the wilcoxon-mann-whitney test, i.e. the version of the pairwise Wilcoxon signed rank test, but with alternative hypothesis?
I don't seem to be able to ...