Types Of Hypotheses Flashcards
What is a random sample in statistics?
A sequence of independent and identically distributed (iid) random variables.
What does iid stand for?
Independent and identically distributed.
What does it mean for variables to be identically distributed?
They come from the same distribution with the same mean and variance.
What is the difference between random variables and observed values?
Random variables are unobserved and capitalized; once observed, values are fixed and not random.
What is the sample mean (X̄)?
The average of all sample values, used to estimate the population mean μ.
What is a null hypothesis (H₀)?
A statement assumed to be true unless evidence suggests otherwise.
What is an alternative hypothesis (H₁ or Hₐ)?
The statement we try to find evidence for; considered if we reject the null.
How is hypothesis testing like a court trial?
The null is ‘innocent until proven guilty’; we can reject or fail to reject it, but never accept it.
How do you choose the null and alternative hypotheses?
H₀ is the status quo; H₁ is what you want to prove or find evidence for.
What kind of hypothesis is μ = 3?
A simple hypothesis, because it specifies a complete distribution.
What kind of hypothesis is μ > 3?
A composite hypothesis, because it includes multiple possible values.
Is a hypothesis with an equal sign always simple?
Not necessarily; it is simple only if all parameters of the distribution are known.
Why is the sample mean used in hypothesis testing?
It is a good estimator of the population mean and reflects underlying data trends.
What does it mean to reject the null hypothesis?
It means the sample provides enough evidence to support the alternative hypothesis.
What does it mean to fail to reject the null hypothesis?
The sample does not provide sufficient evidence to support the alternative.
Can we prove the null hypothesis is true?
No, we can only reject or fail to reject it based on the data.
Why do we need hypothesis testing?
To make decisions about population parameters using sample data.
What kind of test is μ = 3 vs. μ > 3?
A one-sided (right-tailed) test.
What kind of test is μ = 3 vs. μ < 3?
A one-sided (left-tailed) test.
What kind of test is μ = 3 vs. μ ≠ 3?
A two-sided test.
