Mod 3A Statistical Inference and Hypothesis Testing Flashcards
What is the difference between a population and a sample?
A population includes every subject of interest, while a sample is a smaller group drawn from that population to make inferences.
What is point estimation in statistics?
Point estimation involves using sample data to estimate a population parameter like mean (X̄), standard deviation (s), or proportion (P̄).
What is a sampling distribution?
A sampling distribution shows the distribution of a statistic (like sample mean) over many samples from the same population, helping infer population parameters.
What does the Central Limit Theorem state?
It states that the sampling distribution of the sample mean approximates a normal distribution as the sample size becomes large (usually n ≥ 30), regardless of the population’s distribution.
What is interval estimation?
Interval estimation uses a point estimate plus or minus a margin of error to create a range (interval) that likely contains the population parameter.
When is the t-distribution used in hypothesis testing?
The t-distribution is used when the population variance is unknown and the sample size is small; it accounts for more uncertainty than the normal distribution.
What are the null and alternative hypotheses?
The null hypothesis (H0) assumes no effect or no difference; the alternative hypothesis (H1) suggests there is an effect or a difference.
What are Type I and Type II errors in hypothesis testing?
Type I error is rejecting the null hypothesis when it’s true. Type II error is failing to reject the null hypothesis when it’s false.
What does the level of significance in hypothesis testing indicate?
It indicates the probability of committing a Type I error. Common levels are 0.05 (5%) for moderate evidence and 0.01 (1%) for strong evidence against the null hypothesis.
How do you calculate standard error of mean
Standard error = STD / SQRT(N)
How do you calculate standard error of proportion
=SQRT(Sample proportion*(1-Sample proportion)/Total Observations)
How do you calculate sample proportion
= Number of successes / Total Observations
How do you calculate margin of error
=T-value*STD/SQRT(n)
How do you calculate upper and lower bounds
= Sample mean +- margin or error
