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Exercise # 2

Exercise # 2

95% Confidence Interval of Mean

To interpret the confidence interval of the mean, we assume that the values ??were sampled independently and randomly from a normal population with mean $ \ Mu $ and variance $ \ Sigma ^ 2 USD. Since these assumptions are valid, we have 95% “chance” interval contain the true population mean value. In other words, if we produce various confidence intervals from different independent samples of the same size, we expect that approximately 95% of these intervals should contain the true population mean value (Bischoff-Ferrari, Willett, Wong, Stuck, Staehelin, Orav, & Henschkowski, 2009).

A confidence interval (CI) is an estimated range of a parameter of interest in a population. Instead of estimating the value of a single parameter, is given a probable range of estimates.

Confidence intervals are used to indicate the reliability of an estimate. For example, an IC can be used to describe how the results of a study are reliable. All estimates being equal, a search resulting in a small IC is more reliable than one which results in a larger IC.

Therefore, we can interpret the confidence interval as a range that contains the values ??“plausible” that the parameter can take. Thus, the amplitude range is associated with uncertainty as to have a parameter (Hooper, Kroon, Rimm, Cohn, Harvey, Le Cornu, & Cassidy, 2008).

Statistical Power

In statistics, a result is significant and therefore have statistical significance, it is unlikely to have occurred by chance (which in statistics and probability is treated by the concept of chance ), if a particular null hypothesis is true, but it is unlikely if based on the hypothesis is false.

More specifically, the testing of hypotheses based on statistical frequency, the significance of a test is related to the level of confidence in rejecting the null hypothesis priate this is true (a decision known as a Type I error ). The significance level of a result is also called \ Alpha and should not be confused with the value p (p-value).

The level of significance should not be confused with a probability of significance, since there is a probability. For example, in a test with an average, it was possible to repeat a large number of samples to average, about 5% of the samples, the null hypothesis would be rejected when it is true. Thus, as in an actual experiment, only one sample is collected, it is expected that this is a 95% where the null hypothesis is actually false. So has confidence in the outcome.

As another example, to calculate a confidence interval of 95%, equivalent to a Type I error of 5%, we have confidence that the interval contains the estimated parameter. However, since it relates a numerical range, or the unknown population parameter is within or outside the range, there is no probability that the interval contains the parameter (Galiè, Manes, Negro, Palazzini, Bacchi-Reggiani, & Branzi, 2009).

To devise a hypothesis test, the technician should attempt to maximize the ...

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