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Explain the Central Limit Theorem in the context of means.

For a large enough sample size (n ≥ 30), the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

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Explain the Central Limit Theorem in the context of means.
For a large enough sample size (n ≥ 30), the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.
Explain the purpose of the 10% condition.
Ensures independence when sampling without replacement; population size must be at least 10 times the sample size.
What does it mean to 'fail to reject the null hypothesis'?
It means we don't have enough evidence to say the null hypothesis is false, not that it's true.
Explain the purpose of a significance test.
To challenge a claim about a population mean using sample data.
When do you use a t-test?
Use when the population standard deviation (σ) is unknown and you are working with means.
What are the differences between a t-test and a z-test?
t-test: σ unknown, uses sample standard deviation (s), t-distribution | z-test: σ known, population normally distributed, uses z-distribution
What are the differences between Type I and Type II errors?
Type I: Rejecting a true null hypothesis (false positive) | Type II: Failing to reject a false null hypothesis (false negative)
What are the differences between one-sample and two-sample t-tests?
One-sample: Compares the mean of one sample to a known value. | Two-sample: Compares the means of two independent groups.
What are the differences between confidence intervals and significance tests?
Confidence intervals: estimate a population parameter | Significance tests: test a claim about a population parameter
What are the differences between standard deviation and standard error?
Standard deviation: measures the spread of individual data points in a sample. | Standard error: estimates the variability of sample means around the population mean.
What is a null hypothesis?
The claim being tested, often a statement of no effect or no difference.
What is an alternative hypothesis?
What we suspect is true if the null hypothesis is false.
What is a p-value?
The probability of observing a sample mean as extreme as ours (or more extreme) if the null hypothesis were true.
Define a confidence interval.
A range of values that likely contains the true population mean.
What is a t-statistic?
Measures how far our sample mean is from the hypothesized population mean in terms of standard errors.