week8class - The t-distribution Previously, for the sake of...

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The t-distribution Previously, for the sake of convenience, we have been assuming that when dealing with normal models for quantitative data that either μ, or σ, or both are known. In practice, this is never really the case. We have mentioned how the sample mean x is a good (unbiased) estimate of the population mean μ , but now we will also be using s, (the sample standard deviation) , as a measure to estimate the population standard deviation, σ . Recall that: When is not known it is estimated from the sample standard deviation s , and the sampling distribution that results is said to follow a… 2 1 1 ( ) 1 n i s x x n =
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Important properties of the t-distribution: 1. The t distribution is different for different sample sizes 2. The t distribution has the same general symmetric bell shape as the normal distribution but it reflects the greater variability (with wider distributions) that is expected with small samples.
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3. The t distribution has a mean of t = 0 (just as the standard normal distribution has a mean of z = 0). 4. As the sample size n gets larger, the t distribution gets closer to the normal distribution. 5. n s x t / μ = A (1 – α) % confidence interval for μ (when σ is unknown) is defined as:
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Example: The UCLA housing office wants to estimate the mean monthly rent for studios around the campus. A random sample of size n = 36 studios is selected from the area around UCLA. The sample mean is found to be x = $1200 and standard deviation of our sample s = $150. a. Construct a 95% confidence interval for the mean monthly rent of studios in the area around UCLA. b. Construct a 99% confidence interval for the mean monthly rent of studios in the area around UCLA.
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c. How do these intervals compare to the ones we created when we assumed σ was known? In general for all confidence intervals, if everything else remains the same, then:
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Statistical Inference – Hypothesis Testing for Proportions Procedures for statistical inference Point estimation. Appropriate when the goal is to estimate a single best guess at the population parameter. Confidence interval. Appropriate when the goal is to estimate a likely range of values within which the population parameter lies. Hypotheses testing . Hypothesis: a statement about the parameters.
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Concepts of Hypothesis Testing The critical concepts of hypothesis testing: 1. Define your null and alternative hypotheses H o - the null hypothesis H a - the alternative hypothesis It is important to decide upon H a before performing any actual
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This note was uploaded on 11/28/2009 for the course STATS STATS10 taught by Professor Sugano during the Spring '09 term at UCLA.

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week8class - The t-distribution Previously, for the sake of...

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