Discussion C: Central Limit TheoremWeek 5 Post (300+ words):Collect some quantitative data (if your data from week 1 is quantitative, you can use it). Find the sample mean and standard deviation. Plot it in a histogram. Does the data seem to follow the bell curve of the normal distribution? What features of the data do or do not fit in with the shape of the normal curve. How much deviation from the curve is to be expected?Now perform a normality test on your data (Shapiro-Wilk test: http://sdittami.altervista.org/shapirotest/ShapiroTest.html or http://www.brianreedpowers.com/MAT240/stats/descriptiveStats.html)– the test will give you a p-value. The higher the p-value, the more closely your data follows the normal distribution. Based on the test, do you think your data could have been drawn from a normal distribution?Week 6 Responses (100+ words x2):Choose two of your classmates’ data sets. Take 30 random samples of 5 data points each (one way: Past the data here http://www.randomizelist.com/ randomize the list and take the first 5 numbers, or use the sampling feature at http://www.brianreedpowers.com/MAT240/stats/descriptiveStats.html), and calculate the average for each of these samples. You will now have 30 sample means. Create and post a histogram for your sample means. What is the mean of these means? What is the standard deviation? Does this make sense based on the Central Limit Theorem? Do the sample means follow a normal distribution? What p-value does the normality test give? How and why does this differ from the original data?REPLY MY CLASSMATE: Jasmine AliceaThe quantitative data I chose to use was the number hours I slept on an average week, as discussed from my previous post. Finding the mean (or average) of my numbers, simply list all variables in ascending order à 6.5,7,7,7,7.5,8,9. Add all the variable to equal one sum (=52). Then divide by the number of numbers presented. 52/7= 7.428. We want to present the sum to the nearest hundredth; to do so, we need to round up (7.43). To find the median, we need find the middle number between all variables. Fortunately, I have 7 variables and can find the median between the first three numbers and last three numbers (7).Standard DeviationEquation for standard Deviation for sample is as follows:Sample Deviationà Sample(x)=n−1∑∣x−xˉ∣2 = Square root of unbiased sample variancePopulation Deviation equationà σ=N∑(xi−μ)2∑= “sum of”X= is a value in the data setμ=is the mean of the data setN= is the number of data points in the population (not used for this week’s discussion N-1= is used for dealing with a sample variable. (we are using in this week’s discussion)To find the sample subtract the variable by the mean times square- Add them together and then divide by mean.S-(squared)(6.5-7) sq+(7-7)sq+(7-7)sq+(7-7)sq+(7.5-7)sq+(8-7)sq+(9-7)sq7-1n-1 (mean)0.25+0+0+0.25+1+4= 5.5/6= à0.93 Unbiased sample varianceS= sq root of unbiased sample variance à 0.93 squared = 0.86 Sample standard deviationFrequency Histogram4321>=0 2 4 6 8 10I’m not sure if the histogram follows the bell curve of a normal distribution, as I am still trying to see how all the different representations equal the original data; hours I sleep per week. If I am analyzing it visually, I can see how the average time in hours I sleep will be 7, as the spike in the bell curve is narrow and in between 6-9. It does represent a normative distribution.The deviation from the curve is skewed to the right. If my calculations are correct, I sleep on average 7 hours and 45mins but on a good night’s rest 8 ½ hours, and a not-so-great night, 6 hours.The Shapiro-Wilk test is usually recommended for data with <10 variables. It provides a Null Hypothesis (sample size of n comes from a normal distribution).Results: Shapiro-Wilk Normality Testn = 7Mean = 7.428571428571428SD = 0.8380817098475258W = 0.885157374718934Threshold (p=0.01) = 0.7300000190734863 --> HO acceptedThreshold (p=0.05) = 0.8029999732971191 --> HO acceptedThreshold (p=0.10) = 0.8379999995231628 --> HO accepted--> “Your data seems normal”REPLY TO MY CLASSMATE:Tabitha ThuguriThe central limit theorem states that the sampling distribution of any statistic will be normal or nearly normal, if the sample size is large enough. Requirements for accuracy.The more closely the sampling distribution needs to resemble a normal distribution, the more sample points will be required. Requirements for accuracy.The more closely the sampling distribution needs to resemble a normal distribution, the more sample points will be required.

Statistical Concepts for Research questions*** Original answer *** Label and number  each question followed by answer and cite sources below each answer PLS!!!!!1. Paul states that he scored in the 100th percentile on a given standardized test. Do you believe him? Why or why not? 200 word minimum2. Actuaries work with statistics and probabilities each day. What do actuaries do and what tests do they take?(200 word minimum)3. Find a video that provides help with learning probability. Why do you like it and what did you learn? Visit this helpful website (http://www.khanacademy.org/) to assist you with your search. ( provide video link plus 200 word minimum)4. Find a study where the distribution follows a normal or bell-shaped curve. An example of a normal distribution or bell-shaped curve, called “Heights of Red Pine Seedlings”, is located in the beginning of Chapter 6 in the book. Cite the source of the study you’ve selected, and explain why you think the distribution is bell shaped. For instance, if the study is about income, then the income may be low for a child and peak at age forty-five and then gradually drop.