Research method Essay Example | Topics and Well Written Essays - 2000 words

Research method - Essay Example x = ? and ?x = ? * sqrt(1/n - 1/N ) Basing on the mathematical expressions above, it is possible to specify the sampling distribution of the mean unless two conditions are met. First, when the population is said to be normally distributed or otherwise if the sample size is said to be sufficiently large. Secondly, the standard population of the population is known. In this problem, the two conditions are met and, therefore, given the standard deviations, and the means of the five samples given, the mean of the population can be calculated through averaging the sample means. This can be accomplished mathematically, as the population mean = (80934 + 78110.48 + 80,340 + 84716.5)/5 = 64,890.196 $. In a sampling distribution of means, the populations mean (?) has been found to always equal to the sampling distribution (?x) mean. ... From the initial knowledge the standard error of the distribution becomes ?x = ? = 64,890.196$. It is also possible to use the relation ?x = ? * sqrt( 1/n - 1/N to find the standard error of the sampling distribution becomes, which is given by 2943.22 x 0.00137 = 4.03733. Given that the sampling distribution of the mean has been shown to be normally distributed, with a mean of 64,890.196, and the standard error of 4. 03733, in order find the probability that this revenue shall exceed $ 2,2200,000, we shall make use of an online normal distribution calculator. Fitting the these values into a distribution calculator, probability is found to be 0.05. For case II The probability that the revenue shall exceed $, 2,500,000, is found by fitting the values of the standard deviation, the mean and the value $ 2,500,000 into an online normal distribution calculator, which shows that P (