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The significance level is 5% and the number of cases is 60. Power of unpaired and paired two-sample t-tests as a function of the correlation. The simulated random numbers originate from a bivariate normal distribution with a variance of 1 and a deviation of the expected value of 0.4. The significance level is 5% and the number of cases is 60.
Most frequently, t statistics are used in Student's t-tests, a form of statistical hypothesis testing, and in the computation of certain confidence intervals. The key property of the t statistic is that it is a pivotal quantity – while defined in terms of the sample mean, its sampling distribution does not depend on the population parameters, and thus it can be used regardless of what these ...
In a two-tailed test, the rejection region for a significance level of α = 0.05 is partitioned to both ends of the sampling distribution and makes up 5% of the area under the curve (white areas). Statistical significance plays a pivotal role in statistical hypothesis testing.
The five-number summary gives information about the location (from the median), spread (from the quartiles) and range (from the sample minimum and maximum) of the observations. Since it reports order statistics (rather than, say, the mean) the five-number summary is appropriate for ordinal measurements , as well as interval and ratio measurements.
Quite often, textbook problems will treat the population standard deviation as if it were known and thereby avoid the need to use the Student's t distribution. These problems are generally of two kinds: (1) those in which the sample size is so large that one may treat a data-based estimate of the variance as if it were certain, and (2) those ...
the exact sampling distribution of T under the null hypothesis is the binomial distribution with parameters 0.5 and 100. the value of T can be compared with its expected value under the null hypothesis of 50, and since the sample size is large, a normal distribution can be used as an approximation to the sampling distribution either for T or ...
Suppose the data can be realized from an N(0,1) distribution. For example, with a chosen significance level α = 0.05, from the Z-table, a one-tailed critical value of approximately 1.645 can be obtained. The one-tailed critical value C α ≈ 1.645 corresponds to the chosen significance level.
T(y) is the value of the test statistic for an outcome y, with larger values of T representing cases which notionally represent greater departures from the null hypothesis, and where the sum ranges over all outcomes y (including the observed one) that have the same value of the test statistic obtained for the observed sample x, or a larger one.