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MeanVarianceSamplePopulationSizenNIME 301

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b = is a random value = is probability means For example:IME 301Also: For examplemeansThen from standard normal table: b = 1.96

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Point estimator and Unbiased estimator
Confidence Interval (CI) for an unknown parameter
is an interval that contains a set of plausible values of
the parameter. It is associated with a Confidence
Level (usually 90% =

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Confidence Interval for Population Mean Two-sided, t-Interval Assume a sample of size n is collected. Then sample mean, ,and sample standard deviation, S, is calculated. The confidence interval is: IME 301 (new Oct 06)

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Interval length is: Half-width length is: Critical Points are: and IME 301

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Confidence Interval for Population Mean One-sided, t-Interval Assume a sample of size n is collected. Then sample mean, ,and sample standard deviation, S, is calculated. The confidence interval is: OR IME 301 new Oct 06

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Hypothesis: Statement about a parameter
Hypothesis testing: decision making
procedure about the hypothesis
Null hypothesis: the main hypothesis H0
Alternative hypothesis: not H0 , H1 , HA
Two-sided alternative hypothesis, uses
One-sided alternative hypothesis, uses > or

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Hypothesis Testing Process: Read statement of the problem carefully (*) Decide on “hypothesis statement”, that is H0 and HA (**) Check for situations such as: normal distribution, central limit theorem, variance known/unknown, … Usually significance level is given (or confidence level) Calculate “test statistics” such as: Z0, t0 , …. Calculate “critical limits” such as: Compare “test statistics” with “critical limit” Conclude “accept or reject H0”IME 301

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IME 301 FACT H0 is true H0 is false Accept no error Type II H0 error Decision Reject Type I no error H0 error =Prob(Type I error) = significance level = P(reject H0 | H0 is true) = Prob(Type II error) =P(accept H0 | H0 is false) (1 - ) = power of the test

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The P-value is the smallest level of significance that would lead to rejection of the null hypothesis. The application of P-values for decision making: Use test-statistics from hypothesis testing to find P-value. Compare level of significance with P-value. P-value < 0.01 generally leads to rejection of H0 P-value > 0.1 generally leads to acceptance of H0 0.01 < P-value < 0.1 need to have significance level to make a decision IME 301 (new Oct 06)

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Test of hypothesis on mean, two-sided No information on population distribution Test statistic: Reject H0 if or P-value = IME 301

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Test of hypothesis on mean, one-sided No information on population distribution IME 301

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Test of hypothesis on mean, two-sided, variance known population is normal or conditions for central limit theorem holds Test statistic: Reject H0 if or, p-value = IME 301

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Test of hypothesis on mean, one-sided, variance known population is normal or conditions for central limit theorem holds IME 301 and 312