Question

Distinguish between the following:

(a)Confidence level and significance level.(b)Student’s t distribution and sandlers A test(c)Acceptance region and rejection region(d)Power function and operating characteristic function.

Answer 1

Confidence level and significance level

In the theory of statistical tests, the level of significance is the probability of rejecting the null hypothesis when it is true, which is known as a type I error.The confidence interval at the confidence level (1- α)% for a population statistic that contains all the values, when performing hypothesis testing against population statistics, should not be rejected at the α% significance level.Therefore, if a corresponding hypothesis test is performed during the calculation of the confidence interval, it is correct to say that the significance level is 5% if the confidence level is 95%

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Acceptance region and rejection region

All the possible values that a test statistic can assume can be divided into two mutually exclusive groups: a group consisting of values that seem to be consistent with the null hypothesis and the other with values that are unlikely to occur if Ho true. The first group is called an acceptance region and the second set of values is known as a rejection region for a test. The rejection region is also called the critical region. The value (s) that separates the critical region from the acceptance region is called the critical value (s). The critical value, which may be in the same unit as the parameter or in standardized units, must be decided by the experimenter taking into account the degree of confidence that they are willing to have in the null hypothesis.

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Power function and operating characteristic function

A power function is in the form of f(x) = kx^n, where k = all real numbers and n = all real numbers. You can change the way the graph of a power function looks by changing the values of k and n. If n is greater than zero, then the function is proportional to the nth power of x. In a power function, k represents the constant of proportionality. This means that the shape of the line on the graph will not change depending on the value of k, but the placement of the line on the graph will change While in an operating characteristic curve (OC) is a chart that shows the probability of acceptance compared to the percentage of defective items (or lots). Without defects, we will certainly have 100% acceptance! But take a look at 0.05 (5% defective). At this point, there is still 90% acceptance. Thus, the curve begins to fall. No sampling plan will be perfect. The good lots will be rejected and the bad ones will be accepted. There will be a pitcher who makes four shots at home in a game and the stellar beater will snort on every field. If we only sample a single game, it is difficult to trust the strength of our champion. However, if we run more samples, we can have a richer set of data to work with. As a rule, if the curve is steeper, it indicates a better sampling plan.

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