Problem # 1

PROBLEM # 1

In statistics, a hypothesis test is a process of evaluating a statistical hypothesis based on a data set (sample). For example, having observed a number of prints "coin flip" produced by one piece, one wonders if it is biased (that is to say, has a different probability of 1/2 to fall on a given side). In this situation, the hypothesis testing approach is to assume that the coin is unbiased ( null hypothesis ), and calculate the probability of observing runs at least as extreme as that actually observed (using a binomial ). If it is low (in practice, less than a threshold, e.g. 5%), we reject the null hypothesis of equi-probability of the faces of the part, and we decide it is biased.

Within the statistical inference, a hypothesis test (also called hypothesis testing or significance test) is a procedure for judging whether a property is serving a statistical population is consistent with that observed in a sample of that population. It was started by Ronald Fisher and later substantiated by Jerzy Neyman and Karl Pearson. This theory addresses the statistical problem considering a given hypothesis and an alternative hypothesis, And attempts to resolve which of the two is the true hypothesis, after applying the statistical problem to a number of experiments.

It is strongly associated with the considered type I errors and II in statistics, which define respectively the possibility of taking a false event as true, or a true and false. There are several methods to develop such a test, minimizing the errors of type I and II, and finding so with a certain power, the hypothesis with the highest probability of being correct. The most important types are the focus test, and simple alternative hypothesis, randomized, and so on. Among the nonparametric tests, the most widespread is probably the test of the Mann-Whitney.

Question 1

A production process for your firm must fill bottles of pure Bavarian spring water with at least 16.2 ounces. Otherwise, the process is discontinued while adjustments are made. As the resident statistician for the firm, you have been charged with responsibility of determining if the process is working properly. You take a sample of 24 bottles and find a mean weight of 15.7 ounces and a standard deviation of 3.7 ounces. Should you order that the process be shut down for adjustments? You superior will not accept anything less than 99 percent confidence.

Solution

It has been mentioned that ( should be at least 16.2 ounces. Therefore, its hypothesis could be given as follows:

Ho: ( = 16.2H1: ( ( 16.2

Since, we know that the sample size we have taken i.e. 24 is less than 30, therefore, we must use t statistic.

Since the sample size is 24, the degree of freedom would be 24-1 = 23

t0.01,23

tcal or t0.01,23 = 2.500

t = 0.662

t - Statistics

t =

t = (15.7 - 16.2)/3.7

t = 0.662

It can be suggested that the process should not be shut down for adjustments, as the hypothesis is rejected because the magnitude ...