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Flashcards
What is hypothesis testing??
Determining how likely observed data occured by chance.
What is the notation for the null hypothesis??
$$ H_0 $$
What is the notation for the alternate hypothesis??
$$ H_1 $$
What is a population parameter??
A statistic that summarises some information about a population.
In the A-level, what’s the definition of a hypothesis??
Some statement made about a population parameter.
In a binomial distribution, what is the population parameter??
The probability of success, i.e. $p$.
What is the null hypothesis??
The default statement you assume to be true.
In a coin flip experiment, what is the null hypothesis??
That the coin is fair.
What the predicted population parameter be for a coin flip in the null hypothesis??
$$ p = 0.5 $$
In a coin flip experiment, what is the alternate hypothesis??
That the coin is biased.
What can you say about the predicted population paramter for a coin flip in an alternate hypothesis??
$$ p > 0.5 \\ p < 0.5 $$
What do the alternative hypotheses for a one-tailed test look like??
$$ H_1: p > … \\ H_1: p < … $$
What do the alternative hypotheses for a two-tailed test look like??
$$ H_1: p \ne …. $$
How do you carry out a hypothesis test??
Assume the null-hypothesis is true and consider how likely the observed data was to occur.
What is the significance level in hypothesis testing??
The threshold at which you consider a test statistic to be so unlikey as a result of the null hypothesis that you accept the alternative hypothesis.
What is the test statistic in hypothesis testing??
What you observe as a result of doing an experiment.
In a coin flipping experiment to determine if a coin is biased towards heads, what is the test statistic??
The number of observed heads.
What is the critical region in hypothesis testing??
The region on a probability distribution that if the test statistic is within then you reject the null hypothesis.
What is the acceptance region in hypothesis testing??
The region on a probability distribution that if the test statistic is within then you accept the null hypothesis.
What is the critical value in hypothesis testing??
The first value to fall inside the critical region.
If the critical value for an experiment is $r$, how would you write the actual significance level of the hypothesis test??
$$ P(X \ge r) $$
If the given signifance value of a test is $0.05$, what “equation” are you trying to solve in order to find the critical value $r$??
$$ P(X \ge r) > 0.05 $$
What do you do to the signficance value if you’re doing a two-tailed test??
Halve it.
You’re conducting a hypothesis test with significance value $0.05$. $P(X \le 7) = 0.9877$. What’s the critical region??
$$ P(X \ge 8) $$
Why does $P(x \le 7)$ get turned into $P(x \ge 8)$ in hypothesis testing??
Because when working out the cumulative distribution, you have to do $P(X \ge 8) = 1 - P(X \le 7)$
How can you find the critical region for a hypothesis test that uses a cumulative distribution??
Use a probability table or the cumulative distribution calculator.
2012-03-25
What are the 5 steps to carry out a hypothesis test??
- Describe the test statistic
- Identify the null and alternate hypotheses
- Calculate the probability of the test statistic taking the observed value assuming the null hypothesis is true
- Compare this to the significance level
- Write a conclusion in the content of the question
If $X ~ B(10, 0.25)$ and you wish to test $H_1: p > 0.25$ with an observation of $X = 5$ against a $5%$ significance level, what do you need to show??
$$ P(X \ge 5) = 1 - P(\le 4), > 5% $$
If $X ~ B(10, 0.4)$ and you wish to test $H_1: p < 0.4$ with an observation of $X = 1$ against a $5%$ significance level, what do you need to show??
$$ P(X \le 1) < 5% $$
2021-03-30
If you’re asked for the $p$-value or significance value of a two-tailed test, what do you do??
Add the significance values for each tail together.
How do you know when to use $P(X \ge r)$ or $P(X \le r)$ when doing a two-tailed test??
Multiple the sample size by the probability and see if it’s less or greater than the expected value.
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date: 2021-03-16 12:58
tags:
- '@?maths'
- '@?stats'
- '@?public'
title: Stats - Hypothesis Testing