So the variance of your estimate $\hat p$ (which is indeed the sample mean) is $\simeq {1\over n} \hat p(1-\hat p)$ ; you will use this for CI or test procedures. When you sample temperatures, you will have to use both the sample mean and the sample variance for CI and tests. $\endgroup$

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Aug 20, 2022 · The sample proportion is many times noted as $\hat p$ but the hat-p is not a standard notation for proportion estimator, it's a frequent one, not more. I can not find examples right now but I think that the convention of noting the sample proportion as $\hat p$ is not universal and is even a relatively recent one.

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Apr 7, 2019 · We have not discussed $\\hat p$ in my probability and statistics course and a problem involving it is on our hw this week after learning about discrete distributions. The problem states "Let the ran...

Hats and tildes. The convention in (my end of) applied statistics is that $\hat{\beta}$ is an estimate of the true parameter value $\beta$ and that $\tilde{\beta}$ is another, possibly competing estimate.

Apr 17, 2016 · First, remember that an interval for a proportion is given by: p_hat +/- z * sqrt(p_hat * (1-p_hat)/n) With that being said, we can use R to solve the formula like so:

Mar 6, 2022 · A confidence interval based on normal approximation for the Bernoulli where $\hat p(1−\hat p)$ (by the way $\hat p=\bar X_n$) is plugged in for the variance estimator involves two approximations (one by the Central Limit Theorem, the other by variance estimation) and is therefore not equivalent to a test that does not involve variance estimation.

I know how to look up the p-value from a Z score using a Normal distribution table, but I don't know how to calculate it. For example, a question says the alpha equals 5 percent. For example, a question says the alpha equals 5 percent.

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