# Questions tagged [critical-value]

In hypothesis testing, a critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis. If the absolute value of your test statistic is greater than the critical value, you can declare statistical significance and reject the null hypothesis. (source: https://support.minitab.com/)

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### calculating confidence interval for critical value multiplying by negative 1

I am trying to understand how $$\mathbb{P}\left(-z_{\alpha / 2} \leqslant \frac{\bar{X}-\mu}{\sigma / \sqrt{n}} \leqslant z_{\alpha / 2}\right) \approx 1-\alpha$$ can be converted to  \mathbb{P}\...
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### How to find the Chisq values for a two tailed test in R? [duplicate]

How do we find the chisq value for a two tailed test? For left tail we use qchisq(x,df,lower.tail="True") For right tail we use qchisq(x,df,lower.tail="False") What about two ...
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### Simulating critical values using standard Brownian motion

Using R, I am replicating the Table 1 results of this paper https://www.tandfonline.com/doi/abs/10.1080/03610926.2014.985841. I wrote the following ...
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### What critical value should you take to test for cointegration at 5% significance in the Engle-Granger residual-based test?

I am trying to test cointegration relationships between several pairs of stocks, two at a time (all integrated of order 1). First I run the linear models yi=a+byj+e1 and then the reverse yj=a+byj +e2. ...
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### Two ways of writing the critical region for Hypothesis Testing

I have one confusion in writing critical region. Let us suppose that we have a test condition that rejects the the null hypothesis if $T(X) > \chi_{2n,\alpha}$. Can we also write this same test as ...
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### Testing for Cointegration with Dummy Variable (for outlier) in Cointegrating Equation

I have two time series $y_t, x_t$ which are both $I(1)$. I am following the 2-step Engle-Granger approach for testing cointegration between the two series. However, for known reasons, I also want to ...
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### Testing a nonstandard hypothesis: constructing test statistic, finding rejection region and obtaining $p$-value

I have a sample of size $n=1$ (a single observation $x_1$) from a random variable $X\sim N(\mu,\sigma^2)$. The variance $\sigma^2$ is known, but the expectation $\mu$ is unknown. I would like to test ...
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### Is $z_{0.025}$ equal to -1.96, or 1.96?

I'm unsure about the interpretation of $z_{\alpha}$. I've seen some source claim that $z_{\alpha}$ is equal to the z value with $\alpha$ of the area to the right of it. Under this view, $z_{0.025}$ is ...
Let's say you let the Null Hypothesis $H_0$ be that the mean volume of water in a bottle is some $\mu$, and the alternate hypothesis $H_1$ be that the mean volume is not $\mu$. Let's assume you pick a ...