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Introductory Statistics, Lecture 19A, Probability of Type I & II Errors, Power, t-Test
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(0:27) Go through homework problem about calculating probabilities of Type I and Type II error (mail order catalog exercise).
(1:17) Problem description.
(2:51) Start to calculate the probability of a Type I error "alpha" based on the given rejection region (alpha is also called the level of significance).
(3:55) Draw a picture of an area under a Normal curve representing the probability of a Type I error.
(7:06) Finish the calculation.
(8:11) Consequences of making a Type I error in this example.
(8:42) Calculate the probability of a Type II error when mu is assumed to be 28.
(11:43) Calculate the probability of a Type II error when mu is assumed to be 30.
(12:47) Alternative values further from the null values result in greater power (smaller probability of a Type II error).
(13:04) Calculate the power in both of the previous cases.
(13:46) Deciding what alternative value to pick for these calculations in real life.
(14:37) Why are these calculations justified even when the population data are not Normal? Because of the Central Limit Theorem.
(15:02) Exam 2 reminder.
(16:07) Reminders about best study methods.
(17:43) Reminder about a slide related to deriving the formula for binomial coefficients.
(18:25) Weights of male runners example.
(21:25) Find a 95% confidence interval to estimate the population mean weight.
(22:48) Standard error for the mean and its notation.
(25:09) Finish the calculation using df = n - 1 = 23 degrees of freedom and using a spreadsheet to compute the sample mean and sample standard deviation.
(29:34) Interpretation of the answer.
(30:32) Indication of what to do for the requested two-tailed test.
(0:27) Go through homework problem about calculating probabilities of Type I and Type II error (mail order catalog exercise).
(1:17) Problem description.
(2:51) Start to calculate the probability of a Type I error "alpha" based on the given rejection region (alpha is also called the level of significance).
(3:55) Draw a picture of an area under a Normal curve representing the probability of a Type I error.
(7:06) Finish the calculation.
(8:11) Consequences of making a Type I error in this example.
(8:42) Calculate the probability of a Type II error when mu is assumed to be 28.
(11:43) Calculate the probability of a Type II error when mu is assumed to be 30.
(12:47) Alternative values further from the null values result in greater power (smaller probability of a Type II error).
(13:04) Calculate the power in both of the previous cases.
(13:46) Deciding what alternative value to pick for these calculations in real life.
(14:37) Why are these calculations justified even when the population data are not Normal? Because of the Central Limit Theorem.
(15:02) Exam 2 reminder.
(16:07) Reminders about best study methods.
(17:43) Reminder about a slide related to deriving the formula for binomial coefficients.
(18:25) Weights of male runners example.
(21:25) Find a 95% confidence interval to estimate the population mean weight.
(22:48) Standard error for the mean and its notation.
(25:09) Finish the calculation using df = n - 1 = 23 degrees of freedom and using a spreadsheet to compute the sample mean and sample standard deviation.
(29:34) Interpretation of the answer.
(30:32) Indication of what to do for the requested two-tailed test.
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