Statistics Explained Easy 3 - Hypothesis testing and CI's

Explain how to perform a z-test for a mean with known standard deviation, using n=49 and xbar=25, and reject H0 at 0.05, concluding the mean is higher than 20.

Explain a two-sided z-distribution hypothesis test with alpha 0.05 for a 49-day sample testing a mean change from 20 to 25. Conclude by rejecting H0, proving the average temperature changed.

Explore how the p-value, tail areas, and alpha level determine whether to reject the null hypothesis in a two-sided test.

Master hypothesis testing with a z test, using the z distribution, x-bar, confidence intervals, and known sigma against mu0=100; set alpha 0.01; conclude not to reject.

Calculate p-values from the standard normal table and compare two-sided and left-sided rejection regions to decide statistical evidence and whether to reject a claim.

Compute a 90 percent confidence interval for the population mean from the sample, using standard deviation and z critical value, then interpret whether the mean lies within the interval.

Explain a two-sided z-test for a mean with mu0=100, sigma=8, n=16, compute z, p-values, and 95% confidence intervals, and conclude no rejection of the null.

Construct a 95% confidence interval for the population mean using the z-distribution, and see how a value outside the interval leads to rejecting the null hypothesis.

Explain the p-value for a two-sided test by doubling the right-tail probability, compare it to alpha 0.05, and conclude there is not enough evidence to reject the null.

Calculate a 95% confidence interval for the population mean using the sample mean and the standard deviation of x-bar with z=1.96. Verify whether 100 lies inside the interval.

Increasing the sample size from 16 to 64 reduces the standard error of the sample mean, changing the z statistic, the two-sided p-value, and the rejection region.

Examine two-sided hypothesis testing with an x-bar standard deviation of 0.8, identifying rejection regions on both sides, and compute p-values from z-values 2.5 and 2 to form a confidence interval.

Explore how increasing values impact confidence intervals and how larger samples yield more precise estimates of the true population parameter in hypothesis testing.

Perform a one-sided z test comparing Vikings' mean height of 1.85 m to the population mean 1.65 m with n=100. Reject the null at alpha 0.05.

Explain constructing a 90% confidence interval for the population mean using x-bar, the standard deviation of x-bar, and two-sided z-values with the formula.

Explain hypothesis testing with a one-sample t-test when sigma is unknown, using the sample standard deviation and degrees of freedom to determine the t-distribution for a one-sided test.

Compute a 95% confidence interval for the mean using the t-distribution with 15 degrees of freedom, n=16, s=8, yielding a mean near 25 and interval 20.77 to 29.23.

Perform a hypothesis test for mu0 = 100 at alpha 0.01 with normally distributed data; compute the test statistic using the standard error of x-bar and identify right-sided rejection region.

Compute a 90% confidence interval for the population mean using a t distribution with 24 df, yielding 97.16 to 110.84 around mean 104, and check if 100 lies inside.

Explains a two-sided t-test for n=16, with x-bar=102 and mu0=100, using t=(x-bar-mu0)/(s/√n); since t≈1.96 (df=15) we fail to reject the null.

Explain a two-sided hypothesis test and p-values using a t-distribution with 15 degrees of freedom, and illustrate a 95% confidence interval for the mean with x-bar and its standard error.

Illustrates a one-sample hypothesis test using X̄ and s with α=0.05, n=16. Compare the t statistic to the critical value to decide whether to reject H0 that mu equals 10.

Apply chi-square hypothesis testing to assess whether standard deviation remains below 20 milliliters, using a milk beverage example, and interpret degrees of freedom and left-tail p-values.

Demonstrates computing a 95% confidence interval for the standard deviation using chi-square with n−1 degrees of freedom, applying the variance-based formula, and using a calculator or Excel.

Apply the f-test to compare two standard deviations in a hypothesis testing framework, using the f distribution, degrees of freedom, and rejection regions to decide if variances differ.

Discover how to find F critical values from tables by using numerator and denominator degrees of freedom and alpha, and learn reciprocal calculations for left-tail values using the F distribution.