Homework #5 SOC-382 (Fall 2017) Be sure to show all of your work in order and yo
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Homework #5 SOC-382 (Fall 2017) Be sure to show all of your work in order and your interpretations to receive full credit. This homework assignment is due at the beginning of class on Thursday, October 19, This assignment is out of 32 points. 1. Explain the central limit theorem in your own words. What is the significance of this theorem for statistics and data analysis? In other words, what does this theorem allow us to do? (2 points) 2. Problem #2 (a-c) in your textbook (page 174). You only need to calculate the confidence intervals for lower-class respondents. (11 points) 3. Suppose you are interested in obtaining the average number of hours of sleep for all PNVw students. Based on existing research you know that a standard deviation of 4.75 hours is expected due to variations in work and family obligations. You randomly select 150 students the mean amount of sleep among all PNW students? (5 points) Problem #12 (a-c) in your textbook (page 174). (13 points) and determine their mean level of sleep is 6.5 hours. At the 90% confidence level, what is 4.Explanation / Answer
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1) The central limit theorem is a result from probability theory. This theorem shows up in a number of places in the field of statistics.
this theorem allows us to simplify problems in statistics by allowing us to work with a distribution that is approximately normal.
Regardless of the population distribution model, as the sample size increases, the sample mean tends to be normally distributed around the population mean, and its standard deviation shrinks as n increases. Certain conditions must be met to use the CLT.The samples must be independent and The sample size must be “big enough
The unexpected appearance of a normal distribution from a population distribution that is skewed has some very important applications in statistical practice. Many practices in statistics, such as those involving hypothesis testing or confidence intervals, make some assumptions concerning the population that the data was obtained from. One assumption that is initially made in a statisticscourse is that the populations that we work with are normally distributed.
The assumption that data is from a normal distribution simplifies matters but seems a little unrealistic. Just a little work with some real-world data shows that outliers, skewness, multiple peaks and asymmetry show up quite routinely. We can get around the problem of data from a population that is not normal. The use of an appropriate sample size and the central limit theorem help us to get around the problem of data from populations that are not normal.
Thus, even though we might not know the shape of the distribution where our data comes from, the central limit theorem says that we can treat the sampling distribution as if it were normal. Of course, in order for the conclusions of the theorem to hold, we do need a sample size that is large enough. Exploratory data analysis can help us to determine how large of a sample is necessary for a given situation.
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