By Raymond Smullyan

Once more in difficulty with the king and at risk of wasting her head, shrewdpermanent Scheherazade teases the king with a range of 225 devious mathematical and common sense puzzles, together with Go+a5delian mind twisters, paradoxes, metapuzzles, good judgment methods, quantity video games, and extra. 10,000 first printing."

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**Example text**

26 Gaussian density function curve Fig. 27 Density curve and tail probability density of a Gaussian distribution with mean μ and standard deviation σ. The height of the symmetric bell curve is the size of density (not the actual probability) concentrated over the values of the continuous outcome x. The value where the density peaks and the degree of dispersion are completely determined by the mean and standard deviation of the distribution, respectively. The area under the entire density curve becomes 1.

This formulation can easily be extended to comparing a difference in two means to a specified null value of 0 (see Sect. 1). Usually the name of a test comes from the name of the sampling distribution of the test statistic. For example, t-test is the test of which the test statistic follows the t-distribution with a particular degrees of freedom (it will be explained later that the degrees of freedom of the t-distribution is uniquely determined by the sample size, see Sect. 5). A p-value is the probability of observing the test statistic values that are as or more extreme than the currently calculated test statistic value if the null hypothesis H0 was true.

The adopted significance level of a particular test, α, predetermined by the investigator is the maximum allowed probability size of Type-1 error. The maximum allowed probability of Type-2 error size is called β and 1- β is called power of the test. , a singlevalued hypothesis and the test is directional). As depicted, Type-1 error is the area under the density curve of the sampling distribution of the test statistic within the rejection region under the assumption that H0 is true. 05. 05. 05 …” Story telling of technical details of the procedure is unnecessary Do not report the meaningless p-values in the concluding sentences when the p-value is greater than your significance level.