All Flashcards
What is the general form of the null hypothesis?
H₀: μ = μ₀, where μ is the population mean and μ₀ is the hypothesized population mean.
How to calculate the t-statistic for a one-sample t-test?
t = (x̄ - μ₀) / (s / √n), where x̄ is the sample mean, μ₀ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
How to determine the degrees of freedom (df) for a one-sample t-test?
df = n - 1, where n is the sample size.
What is the relationship between α and confidence interval?
Confidence Level = 1 - α. For example, α = 0.05 corresponds to a 95% confidence interval.
Explain the concept of the Central Limit Theorem (CLT) in the context of t-tests.
If the sample size (n) is at least 30, the sampling distribution of the sample mean is approximately normal, allowing us to use the t-distribution.
Explain the importance of random sampling in a t-test.
Random sampling ensures that the sample is representative of the population, allowing for valid inferences about the population mean.
Explain the independence condition in the context of t-tests.
The population size must be at least 10 times the sample size (10n) to ensure that the observations are independent.
Explain the relationship between the p-value and the significance level (α).
If the p-value is less than or equal to α, we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.
Explain Type I error.
Rejecting the null hypothesis when it is true. The probability of committing a Type I error is equal to the significance level (α).
Explain the purpose of checking conditions before performing a t-test.
Checking conditions (randomness, independence, normality) ensures that the assumptions underlying the t-test are met, making the results of the test valid and reliable.
What is the significance level (α)?
The probability of rejecting the null hypothesis when it is actually true (Type I error).
Define the null hypothesis (H₀).
A statement of no effect or no difference, which we are trying to disprove. Expressed as H₀: μ = μ₀.
Define the alternative hypothesis (Hₐ).
The opposite of the null hypothesis. It is what we are trying to find evidence for (μ ≠ μ₀, μ < μ₀, or μ > μ₀).
What is a one-sample t-test?
A test used to compare a sample mean to a known or hypothesized population mean when the population standard deviation (σ) is unknown.
What is the rejection region?
The area under the t-distribution curve where, if our sample statistic falls, we reject the null hypothesis.