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Statistics Hw

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Submitted By chrisramo1
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Statistics
4/29/15
Homework
Question 1 – What is the essence of the confidence interval? Analyze the relationship between the confidence interval and central limit theorem.
Question 2 – Explain the essence of Hypothesis testing. How related are null hypothesis and Alternative Hypothesis. How do you apply confidence interval in hypothesis testing?
Question 3 – Explain the difference between T distribution and Z distribution. When and how do we use T distribution? What is the meaning of the number of degrees of freedom? Left Tail, right tail, 2 tail test: Try to understand the idea of hypothesis testing! Understand how all are participating.

The confidence interval is used by statisticians to express the degree of uncertainty associated with a statistic. It is an interval estimate combined with a probability statement. For example, an interval estimate may be described as 95% confidence interval. This means that if we used the same sampling method to select different samples and we computed an interval estimate for each sample, we would expect the true population range to fall within the interval estimates 95% of the time. Confidence intervals indicate the precision of the estimate and the uncertainty of the estimate. The Central Limit Theorem allows us to define an interval within the sample’s expected range. If samples are drawn from a normal population or if the sample is large enough that xbar is approximately normal by the central limit theorem and standard deviation is known, then the margin of error is calculated using the standard normal distribution. A hypothesis is an assumption about a population parameter. This assumption can be either true or false. Hypothesis testing refers to the procedures used to either accept or reject hypotheses. Generally random samples from the population is gathered. If for some reason, the data is not consistent with

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