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Содержание слайда: 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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Содержание слайда: 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<k
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Содержание слайда: 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 - µy<0 or µx - µy>0
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Содержание слайда: 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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Содержание слайда: 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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Содержание слайда: Terminology
Probability of including the true value of a parameter within a confidence interval
Percentage
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Содержание слайда: Terminology
Two extreme measurements within which an observation lies
End points of the confidence interval
Larger confidence – Wider interval
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Содержание слайда: Estimation of population parameters
Point estimate Interval estimate
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Содержание слайда: Point estimate VS Interval estimate
Point estimate
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Содержание слайда: Point estimate VS Interval estimate
Point estimate
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Содержание слайда: Point estimate VS Interval estimate
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Содержание слайда: Point estimate VS Interval estimate
Point estimate
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Содержание слайда: Point estimate VS Interval estimate
Point estimate
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Содержание слайда: 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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Содержание слайда: The general formula for all confidence intervals are:
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Содержание слайда: 7.5.1 Calculate and interpret confidence intervals for a population parameter
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Содержание слайда: 95% Confidence Interval of the Mean
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Содержание слайда: Common Levels of Confidence
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Содержание слайда: Formula for the Confidence Interval of the Mean for a Specific a
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Содержание слайда: 7.5.1 Calculate and interpret confidence intervals for a population parameter
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Содержание слайда: 7.5.1 Calculate and interpret confidence intervals for a population parameter
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Содержание слайда: 7.5.1 Calculate and interpret confidence intervals for a population parameter
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Содержание слайда: 7.5.1 Calculate and interpret confidence intervals for a population parameter
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Содержание слайда: 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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Содержание слайда: 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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Содержание слайда: 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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Содержание слайда: 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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Содержание слайда: 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.
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Содержание слайда: One-tailed test (left-tailed)
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Содержание слайда: One-tailed test (right-tailed)
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Содержание слайда: Two-tailed test
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Содержание слайда: 7.5.2 Test the hypothesis for a mean of a normal distribution, Ho: µ=k, H1: µ≠k or µ>k or µ<k
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Содержание слайда: 7.5.2 Test the hypothesis for a mean of a normal distribution, Ho: µ=k, H1: µ≠k or µ>k or µ<k
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Содержание слайда: 7.5.3 Test the hypothesis for the difference between means of two independent normal distributions
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Содержание слайда: 7.5.3 Test the hypothesis for the difference between means of two independent normal distributions
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Содержание слайда: 7.5.3 Test the hypothesis for the difference between means of two independent normal distributions
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