Statistical Methods Math Problem Example | Topics and Well Written Essays - 2000 words

Statistical Methods - Math Problem Example 4. Given data: , Sxx = 27100, Syy = 280.1 and Sxy = 2665 Cxx = Sxx - n = 27100 - 10(51.82) = 267.6 Cyy = Syy - n= 280.1 - 10(5.12) = 20 Cxy = Sxy - n= 2665 - 10 (51.8) (5.1) = 23.2 The slope a of the fitted regression line Y on X is a = Intercept b = = 5.1 - (0.0867) (51.8) = 0.6091 Estimate S for the standard deviation of the model s = = 5. H0: A = 0 Vs H1: A 0 where A is the slope of the fitted line Y on X. Test statistic: Under H0, tn - 2 distribution where a is the sample slope parameter, A is the population slope parameter, s is the sample estimate for the standard deviation. The results from Q4 are a = 0.0867, s = 1.4495 and Cxx = 267.6 and A = 0. Test statistic: Pr {-2.306 t8 2.306} = 0.95. The value 0.9786 is contained in this interval and hence we have insufficient evidence to reject the null hypothesis. The p-value is 0.3 which is higher than 0.05. Hence we can conclude that the population slope parameter A = 0. 6. The Fitted line is y = ax* + b where 'a' is the slope and 'b' is the intercept. From previous questions we have the results a = 0.0867 and 0.6091 At x* = 44, the value of the line is y = 0.0867(44) + 0.6091 = 4.424 At x* = 52, the value of the line is y = 0.0867(52) + 0.6091 = 5.118 At x* = 54, the value of the line is y = 0.0867(54) + 0.6091 = 5.291 The 95% confidence interval for mean of Y is given by the formula where a = 0.0867, b = 0.6091, x* = 44, 52 and 54, = 51.8, n = 10, s = 1.4995, Cxx = 267.6 and t8,0.025 = 2.306 At x* = 44, the confidence interval is 4.4239 1.9784 (2.4455, 6.4023) At x* = 52, the confidence interval is 5.1175 1.09428 (4.023, 6.21178) At x* = 54, the confidence... The value 0.9786 is contained in this interval and hence we have insufficient evidence to reject the null hypothesis. The p-value is 0.3 which is higher than 0.05. Hence we can conclude that the population slope parameter A = 0. The tabulated value for t32 distribution at upper 5% significance level is 1.694. Since our test statistic value is higher than this value, we reject H0 at 10% significance level. The tabulated value for t32 distribution at upper 2.5% significance level is 2.037. The test statistic is lower than this. Hence we accept H0 at 5% level of significance. The estimated p-value should be between (0.05, 0.1) excluding the upper and lower limits. The result is statistically significant and we can conclude there is a difference in the mean profit outputs. Since we can only say that the means are not equal and cannot say about which is larger, we recommend carrying out one-sided test and then choosing about which course is best. This is reasonable as the sum of n-1 values of a sample gives the other value of the statistic and there is dependence between the n terms and so the degrees of freedom of sample size n are n - 1. As we infer about 2 samples it is reasonable to use 2(n-1) as degrees of freedom when the sample sizes and variances are equal.

Four Freedoms for All Essay Example | Topics and Well Written Essays - 1500 words

Four Freedoms for All - Essay Example The first freedom, that of speech is the hallmark of a democratic society where people are free to express their opinions on a variety of subjects. Speech differentiates man from any other form of life and allows humans to communicate, and through this communication to explore and create in fields as diverse as music or art, science or medicine. This freedom of speech and expression is not just a basic right, but also a means to impart ideas that contribute to man’s ever increasing knowledge as well as his growth, happiness, and well-being. The curtailment of this freedom can subdue man for a while but in the end, when he sees others enjoying it, revolt is inevitable. In today’s world of speedy communication, this phenomenon is being increasingly seen in the overthrow of dictatorships around the world. In democratic societies, it is the tool used to keep a watch on the activities of those in power, because unbridled power can lead to corruption. This freedom in the hand s of the media is a powerful tool to place facts before the people so they are in a position to make informed choices while choosing their leaders. However, every right comes with a responsibility and freedom of speech does not mean maligning others or their way of life and customs or traditions. A responsible way to use freedom of speech is to respect the rights and freedoms of others. The second freedom is man’s freedom to worship the god or gods of his choice and in a way, he feels fit for his own peace of mind. Today religious intolerance is what is leading to many of the world’s problems. ... It is important to note that a man’s religion or religious beliefs are his personal choice hence it is important for each one of us to have the freedom to choose whom we worship and how we do it. Ultimately all religions preach the same things and they really are the same except for the names that they go by, which again are given to them by man. Religion and religious beliefs have always been the source of conflict since the time man began to worship nature and the elements. Every religion has gone through phases when people were killed and tortured in the name of religion. Most religious leaders are under the impression that the greater the numbers of their followers, the better their religion or the stronger their faith, little realizing that no religious body teaches its followers to kill or steal or lie. Despite this underlying truth that is self evident, religious persecutions have dogged mankind from time immemorial and persist even to this day. International bodies can pass resolutions and nation states can pass laws, but ultimately unless man is willing to admit that religion is a personal choice and cannot be forced on another through fear, real freedom of worship cannot be attained. The third freedom, that of freedom from want is the vast imbalance between the haves and the have nots. There are some countries in our world where poverty is rampant. The people do not have the basic necessities of two square meals a day or a roof over their heads. Here malnourished mothers give birth to underweight babies who do not have a chance to grow into healthy children or adults. Infant mortality rates are high, and those babies who do survive, fall prey to diseases that are spread due to the unhygienic conditions in