Questions tagged [p-value]

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When setting critical regions in two sided hypothesis tests, why assign equal probabilities to both tails?

Consider the problem at https://www.investopedia.com/terms/t/two-tailed-test.asp which states: "A sample of $100$ clients of $ABC$ is taken, and brokerage charges are calculated with the new ...
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2answers
29 views

Comparing P-value and Type 1 Error to reject the null hypothesis

I know, by definition, what p-value and type 2 error mean. However, I have hard time relating those two concepts in rejecting a null hypothesis. Below are my understanding about P-value and Type 1 ...
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36 views

Hypothesis test - p-value [closed]

We want to make an hypothesis test for the mean value $\mu$ of a normal population with known variance $\sigma^2=13456$, using a sample of size $n=100$ that has sample mean value equal to $562$. ...
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3answers
41 views

Testing goodness of fit using Kolmogorov-Smirnov test

I want to check if two probability distributions (experimental and theoretical) are same. The distributions are not normal distributions so I decided to use KS test. I used the MATLAB function KStest2 ...
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2answers
57 views

How to manually calculate the p-value of getting at least 59 heads in 100 coin flips?

This is an example from a video on Khan Academy: Rahim heard that spinning rather than flipping a coin raies the probability of getting heads above 50%. He tested this by spinning 10 different pennies ...
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50 views

Calculating the $p$-value

How do I calculate the $p$ value of the following? Students' height is approximately normal with s.d = $4$ inches, sample = $10$, mean height = $68$ inches. Calculate the $p$ value corresponding to ...
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2answers
57 views

Understanding exact tests for clinical trial data

A clinical trial is done with 400 persons suffering from a particular disease, to find out whether a treatment is better than placebo. They are randomised to receive treatment or placebo (200 ...
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93 views

Is it possible to put inequality to null hypothesis?

Based on a sample of i.i.d. Normal random variables $X_1, . . . , X_n$ with mean µ and variance $σ^2$, propose a test with asymptotic level 5% for the hypotheses: $$ H_0: µ > σ$$ $$ H_1: µ \leq σ$$ ...
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3answers
75 views

Are the null hypothesis and alternative hypothesis mutually exclusive?

I am having a little bit of trouble understanding the concept of p-values. On the one hand, we are saying that the null hypothesis is a hypothesis we set, and the alternative hypothesis is something ...
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1answer
29 views

What test should I use for this problem? (assessing the significance of a change in a categorical variable between two different sized populations)?

I have 2 high schools, School A and School B. For the first school, I have 5 classes of students; for the second, I have 3 classes (so 8 classes in total). Within each class, I have different ...
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1answer
40 views

Finding the p-value between two numbers

I am trying to solve this example in statistics, but my results are different from the ones in the solution and I do not understand why. The example say: A study finds a test statistic $t$-value of $...
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1answer
25 views

Calculating the P-value of a T-distribution.

Learning some statistics here and in the chapter of Linear Regression I wanted to prove the values that I get on summary() from a created model. My ...
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2answers
66 views

Hypothesis testing $p$ value

I have to following question: From a collection of objects numbered $\{1,2,....,K\}$ $20$ objects are picked and replaced. We want to test $H_0: K=100000$ against $H_1 < 100000$, with the ...
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1answer
35 views

Calculating p-value using chi-squared algorithm for an industrial process

I've had a problem assigned to me that ought to have gone to a statistician or process control expert, but it is what it is. Gist of the problem: I need to calculate a p-value from product yield data ...
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48 views

I have a questions about $p$-value and $t$-test

Calculation of $p$-value: Fabric water properties, $H_0: \mu \leq 55\%$ versus $H_A: \mu > 55\%$; $n=15, \bar{x}=59.81\%, s= 4.94\%$ I understand that the hypothesized mean is $55$ samples ...
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22 views

A question on p-value

Given the distribution of the test statistic, we can ask the following question: How unusual or extreme is the observed absolute average difference between treatment and control group assuming the ...
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1answer
42 views

How to calculate a two-sample z-test in python?

I want to calculate the pooled z-test in python, for two-samples. I generated 2D Pareto distributed data, I calculated their probabilities px and py. Now I need to calculate the p-pooled and the z ...
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11 views

probability of false error

The usual approach when dealing with a set of repeated measurements ($x_i$, drawn from a normal distribution centered on μ with standard deviation σ, both unknown) is to employ a (say one-tailed) t-...
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26 views

Help understanding $p$ value?

Say I’m analyzing whether a drug works. My test statistic is the amount of days taken to recover. I split a group of 100 into two, and give one the drug and the other a placebo. So my null ...
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47 views

Hypothesis test for Beta distribution

Suppose I have a probability $p$ of success or failure from a Binomial distribution and I know the true number of successes $D$ from $N$ trials. The probability $p$ comes from some statistical model ...
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1answer
26 views

chi square test goodness of fit (frequency vs % frequency)

I'm trying to use the chi square test goodness of fit to see if heights in a survey are normally distributed. I'm using google sheets to do the calculations. When I look at the charts the distribution ...
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13 views

P values of combined experiment

I have acces to the results of two measurements, call them set $A$ and $B$. Both measurements have measured a quantity $X_i$ with corresponding p-value $p_i$. I am interested in the difference between ...
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23 views

When to stop testing a large data set for a given p-value?

I have a large data set that I need to test. However, the data set is too large to test everything. How how many results out of the data set do I need to test (assuming they all pass) to determine the ...
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16 views

Calculate the p-value (what is the distribution of the proportion without using the Central Limit Theorem)

Let X be a Binomial(20,.6) random variable. Calculate the p-value if the proportion observed was p(hat)=.5 I did the following: P(p(hat)>.5|p=.6)=1-P(p(hat)<=.5|p=.6)...my problem is that, since ...
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25 views

When is it appropriate to calculate the p-value?

I seem to be confused on what is the utility of calculating the p-value. Let's say for the sake of argument, that I'm doing hypothesis testing on a normal distribution with a known $\mu$ and known $\...
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1answer
53 views

P-value Test For Hypothesis

I am working on the following question: For a two-sided t-test to test $H_0: \mu = 6.5$ versus $H_1: \mu \neq 6.5$, based on a sample of size $n$, the test statistic value is $-2.16$ and the $p$-...
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1answer
22 views

Drug hypothesis testing

A drug claims to cure patients in $80$% of all cases. A sample of $10$ patients was taken, $5$ got cured, $5$ not. I need to decide if the manufacturer should change their claim. Assume $5$% to be ...
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1answer
113 views

Show a $p$-value is valid

This is an excercise from "Testing statistical hypotheses" (Lehmann & Romano). Let $\mathcal{X}$ be a sample space, $T$ a test statistic and G be a finite group of transformations (with $M$ ...
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1answer
43 views

What distribution is result of division of two poisson distributed metrics?

I've got two variables A and B with 𝐴≤𝐵 following a Poi(𝜆𝑎), resp. Poi(𝜆𝑏) distribution. Given values a1 and b1 we can figure out if these particular values are significantly decreased by ...
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2answers
63 views

Is there a formula to find the p-value from a given z-score?

I know that you can use a z-table to find p-values given a z-score, however I am curious if you can calculate it without the z-table or a calculator. Is it possible? If so, how do you do it? I've ...
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1answer
27 views

Finding the p_value from a hypothesis testing

I understand that we have a rejection region when all the values of theta are less than 3, such that R={T(X)< c} with c = -z_alpha. I can get the sample mean from the three values: x_bar = 3.29, ...
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1answer
20 views

The highest level of significance at which the null will not be rejected (t-distribution)

How do you determine the highest level of significance (in decimal form) at which the null hypothesis will not be rejected? Let's say for instance I got a p-value of $0.001$ and a test statistic of $...
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103 views

Calculate p-value between two lists of floats of unequal size

I would like to calculate the degree of variance between to lists of floats of unequal size expressed in a p-value. I tried a two-sided t-test as in the example below using python. But answers that ...
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1answer
42 views

Need help understanding hypothesis testing

I have the following question: Let $X_{i}$ be Gaussian random variables with $\mu$ = 10 and $\sigma^{2}$ = 1. We decide to use the test statistic $\hat{\mu}$ = $\frac{1}{20}\sum_{i=1}^{20}X_{i}$...
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1answer
238 views

Regression: width of confidence interval vs t-statistic

My question is about confidence intervals of the slopes estimated in a multivariate regression. I would like to clear up something that is probably a fault somewhere in my understanding. As I ...
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49 views

Devising a hypothesis test for machine failure rate

I'm trying to devise a hypothesis test for failure rate data of machines. The gist is that there are some machines in a factory that run all the time. They fail from time to time and are promptly ...
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2answers
29 views

What if correlation coefficient is much less whereas the p-values is much lesser than the our significance level?

I have a data between rating of the restaurant and the approximate price of food in the restaurant. After doing Hypothesis testing. The pearson correlation coefficient was found to be 0.33 whereas p ...
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1answer
35 views

How will p-values behave when fitting normal/Poisson to binomial?

I know p-values behave uniformly. Now as p(np) is fixed and n goes to infinity, binomial converges to normal(Poisson). Now suppose I take random binomial samplings and fir normal(Poisson) to it, for ...
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1answer
549 views

Find the p value following the exponential distribution $\mu=3$

I want to find the $p$-value (manually) of the following Hypothesis testing. $$H_0:\mu\leq 3 \quad \text{vs} \quad H_1:\mu >3$$ The main thing I know is that $$P(\mathrm{Re}\,j \mid \mu \leq 3)=...
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2answers
34 views

Is P value Type I error in hypothesis testing?

I'm confused about the interpretation of P value in hypothesis testing. I know that we set significance level as 0.05 which is the threshold we set for this test so that it won't suffer from Type I ...
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1answer
271 views

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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0answers
27 views

p-value of specific test

I am trying to solve the following exercise: A control authority needs to test that the probability of getting $0$ at roulette is $1/37$ and bigger. After 1000 trials, they get the number $0$ $40$ ...
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1answer
48 views

p-value of the following test

I have the following problem: I have $X_1 ... X_n$ ~ Bernoulli(p) independent. I also have the following test hypothesis: $H_0: p = p_0$ and $H_1: p > p_0$. I define my test as follows: $T:$ I ...
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1answer
102 views

Making conclusions in a z test for a proportion

A poll from a previous year showed that $10\%$ of smartphone owners relied on their data plan as their primary form of internet access. Researchers were curious if that had changed, so they tested $...
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1answer
79 views

How can I visually estimate, or eyeball, the p-value of a histogram?

The question is: what is the approximate P-value for the investigation of whether mother’s smoking during pregnancy has an effect on the length of gestation. The p-value of this histogram is ...
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213 views

P_Value and Hypothesis testing

Please help me to understand the p-value concept in prospect of Multiple Regression (Backward Elimination). My understanding here is that The null hypothesis is we will assume that the dependent ...
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1answer
38 views

Manual calculation of p-value from chi square and df

I am trying to create an algorithm that could calculate the p-value given the chi-square statistic and the degrees of freedom. I found the following formula here Can anyone please point me in the ...
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1answer
66 views

p-value of a test statistic on a two-sided test

For coursework, I am doing a two-sided test ($H_0 \beta = 0, H_a \beta \neq 0$). The test itself is a generalized likelihood ratio. The test statistic is the ratio LR: $$LR=\frac{L(\beta=0)}{argmax_{\...
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2answers
50 views

Removing variable with big p-value?

I have made a regression with 2 explanatory variables. The summary of that regression shows that one of my variable has a big p-value (0.705). Should I include that variable when writing the the y hat ...
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1answer
33 views

Should a variable with a high p-value exclude from the equation

I have just made a regression with 2 explanatory variables and one dependent variable. One of the variables have a p-value of 0.0303 which I consider significant and the other have a p-value of 0.708. ...