1 / 15

Mean

Mean. Variance. Size. n. Sample. N. Population. IME 301. b = is a random value = is probability. means For example:. means. Then from standard normal table: b = 1.96. Also: For example. IME 301. Point estimator and Unbiased estimator

thor-slater
Télécharger la présentation

Mean

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Mean Variance Size n Sample N Population IME 301

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

  3. 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% =<CL=< 99%) , which measures the probability that the confidence interval actually contains the unknown parameter value. CI = – half width, + half width An example of half width is: • CI length increases as the CL increases. • CI length decreases as sample size, n, increases. • Significance level ( = 1 – CL) IME 301

  4. 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)

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

  6. 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

  7. 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 < IME 301

  8. 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

  9. FACT H0 is trueH0 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 IME 301

  10. 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)

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

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

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

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

More Related