Statistics: Confidence Intervals & Hypothesis Testing

Confidence Intervals & Hypothesis Testing

• A 95% confidence interval of (-209.800, -17.700) indicates upperclassmen pay significantly more in rent than underclassmen.
• A confidence interval of (-0.11, -0.03) shows a significant decrease in the proportion of Americans believing education spending is too low from 1988 to 2008.
• Dependent samples are used when comparing means of paired observations, such as leg strength.
• A 95% confidence interval for blood pressure difference (-21, -6) indicates a significant reduction when following a diet.
• A test statistic of 3.45 suggests strong evidence that the average weight loss in a diet program is greater than zero.
• In a shelf life study, a confidence interval of (-0.7, 0.1) signals insufficient evidence of a difference between two brands of doughnuts.

Samples & Data Types

• To compare resting heart rates of runners and bikers, use independent samples of two means.
• For heart disease prevalence in caffeinated drinkers, the analysis involves two independent proportions.
• To assess walking distance between Europeans and Americans, comparing means from independent samples is appropriate.

Regression & Correlation

• In a regression analysis predicting electricity usage, larger homes are expected to consume more electricity, indicating a positive slope.
• A correlation of 0.49 suggests a weak positive linear association between box office receipts and nominations for best picture.
• Time spent exercising and height shows no association in younger individuals aged 18-32.
• Correlation strengths indicate weaker relationships as values approach zero, not confined between 0 and 1.

Chi-Square Tests

• For associations between categorical variables (e.g., sex and blood type), a chi-squared test of independence is conducted, with a null hypothesis asserting no association.
• The chi-squared statistic equals zero when all observed counts match expected counts.
• As sample size increases, the margin of error in confidence intervals decreases.

General Concepts

• Confidence intervals estimate parameter values from sample data.
• Hypothesis testing evaluates claims about population parameters, like the mean significantly differing from a set value.
• A t-distribution is often utilized when working with small sample sizes.

Miscellaneous Associations

• A positive association between two quantitative variables indicates an increasing trend, while a negative correlation reflects a decreasing trend.
• A positive correlation exists when sales of ice cream correlate with temperature, highlighting environmental factors in consumer behavior.