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Confidence interval and Hypothesis testing for population mean (µ) when is known and n (large), слайд №1

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NUFYP Mathematics & Computing Science Pre-Calculus Course L21 Confidence interval and Hypothesis testing for population mean (µ) when is known and n (large)

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Lecture overview: Learning outcomes At the end of this lecture you should be able to: 7.6.1 Calculate and interpret confidence intervals for a population parameter 7.6.2 Test the hypothesis for a mean of a normal distribution, Ho: µ=k, H1: µ≠k or µ>k or µ

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Lecture overview: Learning outcomes At the end of this lecture you should be able to: 7.6.3 Test the hypothesis for the difference between means of two independent normal distributions Ho: µx - µy=0, H1: µx - µy≠0 or µx - µy0

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Textbook Reference The content of this lecture is from the following textbook: Chapter 3 Statistics 3 Edexcel AS and A Level Modular Mathematics S3 published by Pearson Education Limited ISBN 978 0 435519 14 8 Further examples can be found in the textbook.

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Terminology A range of values constructed so that there is a specified probability of including the true value of a parameter within it

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Terminology Probability of including the true value of a parameter within a confidence interval Percentage

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Terminology Two extreme measurements within which an observation lies End points of the confidence interval Larger confidence – Wider interval

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Estimation of population parameters Point estimate Interval estimate

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Point estimate VS Interval estimate Point estimate

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Point estimate VS Interval estimate Point estimate

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Point estimate VS Interval estimate

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Point estimate VS Interval estimate Point estimate

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Point estimate VS Interval estimate Point estimate

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7.5.1 Calculate and interpret confidence intervals for a population parameter Interval estimate provides us interval within which we believe value of true population mean falls Then by using Standard Normal Distribution we can consider specific level of confidence that µ is really there by adjusting critical coefficient

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The general formula for all confidence intervals are:

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7.5.1 Calculate and interpret confidence intervals for a population parameter

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95% Confidence Interval of the Mean

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Common Levels of Confidence

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Formula for the Confidence Interval of the Mean for a Specific a

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7.5.1 Calculate and interpret confidence intervals for a population parameter

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7.5.1 Calculate and interpret confidence intervals for a population parameter

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7.5.1 Calculate and interpret confidence intervals for a population parameter

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7.5.1 Calculate and interpret confidence intervals for a population parameter

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7.5.2 Test the hypothesis for a mean of a normal distribution Hypothesis testing as well as estimation is a method used to reach a conclusion on population parameter by using sample statistics.

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7.5.2 Test the hypothesis for a mean of a normal distribution In Hypothesis testing beside sample statistics level of significance (α) is used to make a meaningful conclusion.

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The level of significance, a, is a probability and is, in reality, the probability of rejecting a true null hypothesis. The level of significance, a, is a probability and is, in reality, the probability of rejecting a true null hypothesis. Confidence level C = (1- a) Level of Significance a = 1 - C

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7.5.2 Test the hypothesis for a mean of a normal distribution In Hypothesis testing we compare a sample statistic to a population parameter to see if there is a significant difference.

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Types of Hypothesis testing Null Hypothesis (H0) Alternative Hypothesis (Ha or H1) Each of the following statements is an example of a null hypothesis and corresponding alternative hypothesis.