Central Limit Theorem Essay

He author also uses statistics to inform the readers with facts. For example he says, “If you’re like the typical owner, you’ll be pulling your phone out 80 times a day.” He uses statistics to inform and persuade the the

As discussed in the previous section, a normal distribution has particular characteristics it conforms to. i.e.

·  How were measures of central tendency used in the study? Did the study use the most appropriate measure of central tendency for the given data? Why or why not?

• Provide at least two examples or problem situations in which statistics was used or could be used.

12. _____ For a given population, confidence intervals constructed from larger samples tend to be narrower than those constructed from smaller samples. Which statement below best describes why this is true? (A) The variability of the sample mean is less for larger samples. (B) The z-value for larger samples tends to be more accurate. (C) The population variance is larger for large populations. (D) As the sample size increases, the z-value (or t-value) becomes smaller. A machine dispenses potato chips into bags that are advertised as containing one pound of product. To be on the safe side, the machine is supposed to be calibrated to dispense 16.07 ounces per bag, and from long time observation, the distribution of the fill-weights is known to be approximately normal and the process is known to have a standard deviation of 0.15 ounces.

If the population was distributed normally the sample size to be taken will decrease. As the population normally distributes the variance and standard deviation population means will decrease so less number of sample would be appropriate to give good estimates of disease severity to determine the disease epidemics.

The law of large numbers, according to Yakir (2011) is the principle of probability that defines the sampling distribution of the average or mean for large samples. The more the number of trials increases, the more the actual proportion of events converges on the hypothetical ratio of outcomes. (p. 115-116)

Iterations of analysis eliminated data points that were listed as “unusual observations,” or any data point with a large standardized residual. After 5 iterations, the analysis showed improved residual plots. Randomness in the versus fits and versus order plots means that the linear regression model is appropriate for the data; a straight line in the normal probability plot illustrates the linearity of the data, and a bell shaped curve in the histogram illustrates the normality of the data.

18. Suppose that the scores of architects on a particular creativity test are normally distributed. Using a normal curve table, what percentage of architects have Z scores:

standard deviation standardized value rescaling z-score normal model parameter statistic standard Normal model 68-95-99.7 Rule normal probability plot

Explain. I don’t think that mine has normal distribution. Mine has a wide range of numbers, but I don’t think that it is distributed like a normal graph should be distributed

It is one of the most popular and well known measures of central tendency. It can be used with both discrete and continuous data, although its use is most often with continuous data

The story began in a sunny afternoon in Cambridge in the 1920s. A group of scientists was having a tea party when a lady claimed that there was a difference in taste between the cups where tea was poured into milk and the cups where milk was poured into tea. Sir Ronald Fisher who became a famous statistician suggested an experiment to test the lady’s hypothesis. The story then goes to the 1890s when the statistical revolution started. Karl Pearson was considered by many as the founder of mathematical statistics. Pearson discovered the skew distributions stating that they would cover any type of data scatter and he described these distributions by four numbers; mean, standard deviation, kurtosis and symmetry. Later a Polish mathematician, Jerzy Neyman showed that Pearson’s skew distributions can not be used to explain all possible distributions. Sir Francis Galton who discovered fingerprints was also interested in statistics and he founded a biometrical laboratory to measure height and weights in families to find a mathematical formula that predict the height of children from the heights of their parents. He described regression to the mean where heights of the children moved away from

Statistical dispersion is measured by a number system. The measure would be zero, if all the data were the same. As the data varies, the measurement number increases. There are two purposes to organizing this data. The first is to show how different units seem similar, by choosing the proper statistic, or measurement. This is called central tendency. The second is to choose another statistic that shows how they differ. This is known as statistical variability. The most commonly used statistics are the mean (average), median (middle or half), and mode (most frequent data). After the data is collected, classified, summarized, and presented, then it is possible to move on to inferential statistics if there is enough data to draw a conclusion.

Why does the sampling distribution of the mean follow a normal distribution for a large enough sample size, even though the population may not be normally distributed?