Test of Hypothesis, Simplified Example-Based Approach

Learn how confidence intervals form an acceptance region around the mean in a two-sided test, using a 95% level to decide whether to reject the null hypothesis.

Compute the two-sided p-value from the standard normal distribution for the observed statistic. Compare this p-value to alpha to decide whether to reject the null hypothesis about the population mean.

Apply confidence intervals, z-values, and p-values to test hypotheses and decide when to reject the null hypothesis, noting that different methods lead to the same conclusions.

Apply a one-sided hypothesis test to determine if the mean temperature exceeds 45 degrees using a 95% confidence level, with a one-sided rejection region and the standard normal test statistic.

Use the t distribution to test hypotheses when population variance is unknown, replacing it with the sample variance and n-1 degrees of freedom; illustrate with a diode threshold voltage example.

Learn to use two-sided confidence intervals and p-values to test hypotheses, applying t distribution with n-1 degrees of freedom and normal approximation for large samples.

Analyze a one-sided hypothesis test with a large sample size, comparing t and normal distributions, using alpha, critical values, and confidence intervals to decide whether to reject the null.

Learn how to select sample size to balance type I and type II errors, maximize power, and use operating characteristic curves for one- and two-sided tests with practical examples.

Apply a one-sided chi-square test to assess if the noise variance exceeds 2.5 in a communication channel, using a sample variance of 3.5, df=29, and 5% alpha, leading to rejection.

Construct confidence intervals for population variance with chi-square methods and interpret p-values for one- and two-sided variance tests, using critical values and rejection regions.

Conduct a variance test with n=30 and sample variance 3.8 against a 2.5 threshold at 95 percent confidence, and reject the null when the p value is less than alpha.

Explore the MATLAB 2013 interface, including the command window, workspace, current folder, and command history. Demonstrate basic operations, variable assignments, and how to clear the workspace and command window.

Learn how to create and run MATLAB M-Files, manage variables with clear and semicolon commands, and plot the standard normal distribution while shading the area under the curve.

Perform a one-sample z test in Matlab for mu = 500 with known variance on nine samples at 95% confidence; a two-sided test shows we fail to reject the null.

Compute a confidence interval for a z test in Matlab, using norm to find lower and upper limits, and decide to reject or fail to reject the null accordingly.