Introduction to Statistics: Hypothesis Testing

Estimate a population proportion using p-hat from a random sample, build confidence intervals with margin of error, and apply z or t critical values for common confidence levels.

Estimate the population mean from a random sample, determine the margin of error, and use the t distribution when sigma is unknown and the z distribution when sigma is known.

Learn to estimate population standard deviation and variance using the sample standard deviation and the chi-square distribution, with normality checks and chi-square confidence intervals based on n-1 degrees of freedom.

Learn the basics of hypothesis testing, including null and alternative hypotheses, two-tailed and one-tailed tests, type I and II errors, p-values, significance level, and decision rules.

Learn how to perform one-proportion hypothesis tests using p-hat, p0, and p-values, with binomial and normal approximations, and interpret results for claim about a proportion.

Learn to test a claim about a population mean with two-tailed t or z tests, form null and alternative hypotheses, and decide via p-values or critical values.

Test a claim about a population standard deviation or variance using chi-square. Determine hypotheses, select alpha, compute chi-square statistic with degrees of freedom, and decide via p-value or critical value.

Learn to compare two population proportions using independent samples, perform two-proportion hypothesis tests, set significance levels, compute p-values, and construct confidence intervals for the difference.

Explore hypothesis testing for two independent population means, using two-sample t tests and confidence intervals, with p-values, alpha levels, and decision rules.

Perform a paired t-test for dependent samples, computing the mean difference (D-bar) and its standard deviation, then interpret the p-value and confidence interval.

Assess equality of two population variances using the F test, checking independence and normality, computing the p value against alpha, and drawing conclusions about variance differences.