Chapter 12: Hypothesis Tests applied to means 1

Experimental hypothesis

A prediction that states how an independent variable will affect a dependent variable in an experiment

(e.g., "Increased study time will lead to higher test scores")

Central Limit Theorem

A statistical principle stating that the sampling distribution of the mean approaches a normal distribution as sample size increases, regardless of the population's distribution

(e.g., averages of large random samples tend to be normally distributed)

Student’s t distribution

A probability distribution used for hypothesis testing when the sample size is small and the population standard deviation is unknown

(e.g., used to calculate t-values in small sample tests)

Interval estimate

A range of values, derived from sample data, that is likely to contain the true population parameter with a certain level of confidence

(e.g., a 95% confidence interval for a mean score)

Confidence limits

The upper and lower bounds of a confidence interval, indicating the range within which the true population parameter is likely to fall

(e.g., a 95% confidence interval with limits of 50 to 60 means the true value is likely between 50 and 60)

Confidence interval

A range of values, calculated from sample data, that is likely to contain the true population parameter with a specified level of confidence

(e.g., a 95% confidence interval for a mean might be 45 to 55, suggesting the true mean is likely between 45 and 55)

Degrees of freedom

The number of independent values or observations that are free to vary in a statistical analysis, typically one less than the sample size

(e.g., for a sample of 10 data points, there are 9 degrees of freedom when estimating variance)

Effect size

A measure of the strength or magnitude of a relationship or difference in a study, helping to understand the practical significance of the results

(e.g., Cohen's d indicates the size of the difference between two groups)

Point estimate

A single value derived from sample data used to estimate a population parameter

(e.g., the sample mean used to estimate the population mean)