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 ...
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 ...
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 $562$. ...
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 ...
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 ...
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 ...
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 ...
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: $$H_0: µ > σ$$ $$H_1: µ \leq σ$$ ...
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 ...
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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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 $p$-...
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 ...
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 $M$ ...
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 ...
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 ...
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, ...
20 views