![]() Size, which in this case is going to be 15, so Underestimate the margin of error, so it's going to be t star times the sample standard deviation divided by the square root of our sample The t distribution here because we don't want to ![]() Now in other videos we have talked about that we want to use So we're going to go take that sample mean and we're going to go plus or But we also want to constructĪ 98% confidence interval about that sample mean. Here we're going to take a sample of 15, so n is equal to 15, and from that sample we can calculate a sample mean. ![]() There's a parameter here, let's say it's the population mean. Of what's going on here, you have some population. Report the values and interpret their implications for the null hypothesis.What is the critical value, t star or t asterisk, for constructing a 98% confidence interval for a mean from a sample size of n isĮqual to 15 observations? So just as a reminder. ![]() Determine the observed test-statistic value and its exact significance level.Modern Approach (used when using statistical software):.If it isn't, do not reject the null hypothesis. Decision: If the observed test-statistic value is in the critical region, reject the null hypothesis Ho.Determine if the observed test-statistic value is in the critical region.Calculate the test-statistic value (this is the "observed" test statistic value).Determine the (estimate of the) standard error of the mean.Classical approach (used when doing problems by hand):.This step is the same for both one-sample tests. The distribution depends on the " degrees of freedom".įor the one-sample T-test, the degrees of freedom is simply equal to one less than the sample size. There is a whole family of distributions. Notice that there is a new complication in using T: There isn't just one T-distribution that we use to determine the critical value of T. T-Test: We use the alpha-level and the degrees of freedom to find the critical T value in the T table. Z-Test: We use the alpha-level to find the critical Z value in the Z table. This is the same for both one-sample tests. (Classical Approach): Set the decision criteria.This hypothesis states that there is an effect (two-tail), or that the effect is in an anticipated direction (one-tail). Ho: The null hypothesis This states there is no effect (two-tail), or that the effect is not in the direction we anticipate (one-tail).The details of some of the steps differ: The method of determining the critical region depends which one-sample test we are using, and, of course, we way we calculate the (estimate of the) standard error differs for T and Z. The overall process of hypothesis testing is the same whether or not we know the population standard deviation/variance: We have the same four steps. Review of The Logic of Hypothesis Testing.If we don't know the population standard deviation or variance we compute a t-test statistics. If we know the population standard deviation or variance we compute a z-test statistic. To quantify our inferences about the population, we compare the obtained sample mean with the hypothesized population mean.The formula for the estimate of the standard error is: If we don't know the population standard deviation or variance we use the sample's standard deviation or variance to obtain an estimate of the standard error. If we know the population standard deviation or variance, the standard error formula is: The standard error provides a measure of how well a sample mean approximates the population mean.This permits us to use the sample mean to test a hypothesis about the population mean. A sample mean is expected to more or less approximate its population mean.These statistical procedures were based on a few basic notions, which are summarized as follows: Review of One-Sample Tests Chapter 8 and Chapter 9 presented the statistical procedures that permit researchers to use a single sample mean to test hypotheses about a population.Two Sample T-Tests Copyright © 1997 by Forrest W.
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