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What is the meaning of p-hat?
P-hat coveys the sample proportion, the ratio of certain events or characteristics occurring in a sample to the sample size. It can equal or differ from population proportion, which conveys a proportion of a particular feature associated with a population.
What does it mean if p-hat equals 0.6 in a political poll?
If p-hat equals 0.6 in a political poll, 60% of voters from the sample support a particular event or a candidate. P-hat is the ratio of the number of occurrences of a particular event to the sample size and is often reported as a percentage in polls.
How do I find p-hat?
To find p-hat (i.e., sample proportion), you need to follow the next steps:
- Take the number of occurrences of an event or the number of successful outcomes.
- Divide it by the sample size.
- That's all! You have calculated p-hat.
Hello, I'm going through MIT OCW 18.06 and I'm stuck on this problem from lecture 1.5.
I understand part A just fine, but I don't understand B. This is the solution that they give, but I'm unclear what it even means. What would I google to figure out what p hat is? Is this some sort of recursive matrix?
In the frequentist tradition (which is what you are using here) the random variable is the data. The population parameters are mathematically treated as constant. This is what leads to the somewhat counterintuitive "null hypothesis" setup we use in intro statistics, because the probability we return (usually in the form of a p-value) is a probability on the sample given constant population parameter set at the null hypothesis values.
I would imagine this is why you see the notation you do in introductory many textbooks.
I don't see a $\hat{p}$ in the figure you posted, but from the formula in the figure, $p_1$ and $p_2$ are statistics. Once you calculate a statistic, it becomes a realization of the random variable (Be aware that I am not saying that your statistic is the true population parameter).
Above all, remember that in most cases upper/lower cases are conventions. They might be widespread, which can be helpful in many cases, but there is no law that forces you to write a random variable's "name" in uppercase. It's common for introductory (and even advanced) books to have a discussion on symbols and style. That section will help you understand the notation the author(s) has adopted.