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Sesión 05 doctor Jorge Ramírez Medina

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1. 1. Sesión 5 Intervalos de Confianza y pruebas de Hipótesis Estadística en las organizaciones CD4001 Dr. Jorge Ramírez Medina
2. 2. Estimación de intervalo de la media de una Población : s desconocida • Si no se puede tener un estimado de la desviación estándar de la población s se utiliza la desviación estándar s de la muestra para estimar s . • En este caso, la estimación del intervalo para m está basada en la distribución t. Dr Jorge Ramírez Medina EGADE Business School
3. 3. Pruebas de hipótesis • Una cola – Cola superior – Cola inferior s conocida s desconocida • Dos colas Reject H0 a  s conocida s desconocida Do Not Reject H0 z Dr Jorge Ramírez Medina EGADE Business School
4. 4. Hipótesis nula y alternativa  Hypothesis testing can be used to determine whether a statement about the value of a population parameter should or should not be rejected.  The null hypothesis, denoted by H0 , is a tentative assumption about a population parameter.  The alternative hypothesis, denoted by Ha, is the opposite of what is stated in the null hypothesis.  The alternative hypothesis is what the test is attempting to establish. Dr Jorge Ramírez Medina EGADE Business School
5. 5. Planteamiento de Hipótesis • Testing Research Hypotheses • The research hypothesis should be expressed as the alternative hypothesis. • The conclusion that the research hypothesis is true comes from sample data that contradict the null hypothesis. Dr Jorge Ramírez Medina EGADE Business School
7. 7. Type I and Type II Errors Errores Population Condition Conclusion H0 True (m < 12) H0 False (m > 12) Accept H0 (Conclude m < 12) Correct Decision Type II Error Type I Error Correct Decision Reject H0 (Conclude m > 12) Dr Jorge Ramírez Medina EGADE Business School
8. 8. Error Tipo I  Because hypothesis tests are based on sample data, we must allow for the possibility of errors.  A Type I error is rejecting H0 when it is true.  The probability of making a Type I error when the null hypothesis is true as an equality is called the level of significance.  Applications of hypothesis testing that only control the Type I error are often called significance tests. Dr Jorge Ramírez Medina EGADE Business School
9. 9. Error Tipo II  A Type II error is accepting H0 when it is false.  It is difficult to control for the probability of making a Type II error.  Statisticians avoid the risk of making a Type II error by using “do not reject H0” and not “accept H0”. Dr Jorge Ramírez Medina EGADE Business School
10. 10. Summary of Forms for Null and Alternative Hypotheses about a Population Mean  The equality part of the hypotheses always appears in the null hypothesis.  In general, a hypothesis test about the value of a population mean m must take one of the following three forms (where m0 is the hypothesized value of the population mean). H 0 : m  m0 H a : m  m0 H 0 : m  m0 H a : m  m0 H 0 : m  m0 H a : m  m0 One-tailed (lower-tail) One-tailed (upper-tail) Two-tailed Dr Jorge Ramírez Medina EGADE Business School
11. 11. p-Value para la prueba de Hipótesis de dos colas  Compute the p-value using the following three steps: 1. Compute the value of the test statistic z. 2. If z is in the upper tail (z > 0), find the area under the standard normal curve to the right of z. If z is in the lower tail (z < 0), find the area under the standard normal curve to the left of z. 3. Double the tail area obtained in step 2 to obtain the p –value.  The rejection rule: Reject H0 if the p-value < a . Dr Jorge Ramírez Medina EGADE Business School
12. 12. p-Value para la prueba de Hipótesis de dos colas  The critical values will occur in both the lower and upper tails of the standard normal curve.  Use the standard normal probability distribution table to find za/2 (the z-value with an area of a/2 in the upper tail of the distribution).  The rejection rule is: Reject H0 if z < -za/2 or z > za/2. Dr Jorge Ramírez Medina EGADE Business School
13. 13. Pasos de la prueba de Hipótesis Step 1. Develop the null and alternative hypotheses. Step 2. Specify the level of significance a. Step 3. Collect the sample data and compute the test statistic. p-Value Approach Step 4. Use the value of the test statistic to compute the p-value. Step 5. Reject H0 if p-value < a. Dr Jorge Ramírez Medina EGADE Business School
14. 14. Pasos de la prueba de Hipótesis Critical Value Approach Step 4. Use the level of significanceto determine the critical value and the rejection rule. Step 5. Use the value of the test statistic and the rejection rule to determine whether to reject H0. Dr Jorge Ramírez Medina EGADE Business School
15. 15. Ejemplo: Pasta de dientes • Two-Tailed Test About a Population Mean: sKnown The production line for Glow toothpaste is designed to fill tubes with a mean weight of 6 oz. Periodically, a sample of 30 tubes will be selected in order to check the filling process. Quality assurance procedures call for the continuation of the filling process if the sample results are consistent with the assumption that the mean filling weight for the population of toothpaste tubes is 6 oz.; otherwise the process will be adjusted. Dr Jorge Ramírez Medina EGADE Business School
16. 16. Ejemplo: Pasta de dientes  Two-Tailed Test About a Population Mean: s Known Assume that a sample of 30 toothpaste tubes provides a sample mean of 6.1 oz. The population standard deviation is believed to be 0.2 oz. Perform a hypothesis test, at the .03 level of significance, to help determine whether the filling process should continue operating or be stopped and corrected. Dr Jorge Ramírez Medina EGADE Business School
17. 17. Prueba de dos colas de µ: s conocida  p –Value and Critical Value Approaches 1. Determine the hypotheses. H0: m6 Ha: m  6 2. Specify the level of significance. a = .03 3. Compute the value of the test statistic. x  m  6.1  6  2.74 z s / n .2 30 0 Dr Jorge Ramírez Medina EGADE Business School
18. 18. Prueba de dos colas de µ: s conocida  p –Value Approach 4. Compute the p –value. For z = 2.74, cumulative probability = .9969 p–value = 2(1  .9969) = .0062 5. Determine whether to reject H0. Because p–value = .0062 < a = .03, we reject H0. We are at least 97% confident that the mean filling weight of the toothpaste tubes is not 6 oz. Dr Jorge Ramírez Medina EGADE Business School
19. 19. Prueba de dos colas de µ: s conocida  p-Value Approach 1/2 p -value = .0031 1/2 p -value = .0031 a/2 = a/2 = .015 .015 z z = -2.74 -za/2 = -2.17 Dr Jorge Ramírez Medina EGADE Business School 0 za/2 = 2.17 z = 2.74
20. 20. Prueba de dos colas de µ: s conocida  Critical Value Approach 4. Determine the critical value and rejection rule. For a/2 = .03/2 = .015, z.015 = 2.17 Reject H0 if z < -2.17 or z > 2.17 5. Determine whether to reject H0. Because 2.47 > 2.17, we reject H0. We are at least 97% confident that the mean filling weight of the toothpaste tubes is not 6 oz. Dr Jorge Ramírez Medina EGADE Business School
21. 21. Prueba de dos colas de µ: s conocida  Critical Value Approach Sampling distribution of z  x  m 0 s/ n Reject H0 a/2 = .015 -2.17 Dr Jorge Ramírez Medina EGADE Business School Reject H0 Do Not Reject H0 a/2 = .015 0 2.17 z
22. 22. Prueba de Hipótesis de µ: s desconocida • Test Statistic t x  m0 s/ n This test statistic has a t distribution with n - 1 degrees of freedom. Dr Jorge Ramírez Medina EGADE Business School
23. 23. Prueba de Hipótesis de µ: s desconocida  Rejection Rule: p -Value Approach Reject H0 if p –value < a  Rejection Rule: Critical Value Approach H0: mm H0: mm Reject H0 if t > ta H0: mm Dr Jorge Ramírez Medina EGADE Business School Reject H0 if t < -ta Reject H0 if t < - ta or t > ta
24. 24. Examen de la sesión • Seis preguntas • Límite de tiempo para contestar el examen 1hr. • Puede utilizar computadora, apuntes y formatos de Excel • No puede consultar con sus compañeros • Al iniciar el examen no es permitido comunicarse electrónicamente ni personalmente.. Dr. Jorge Ramírez Medina EGADE Business School
25. 25. Casos a resolver en Clase Resuelva en equipos los dos casos para clase 1. Salarios de inicio para MBA 2. Máquina industrial de relleno de líquido Las indicaciones se las dará el profesor en la sesión de clase. Suba sus resultados de manera individual en la plataforma. Dr. Jorge Ramírez Medina EGADE Business School
26. 26. Asignación para la siguiente sesión Dr. Jorge Ramírez Medina EGADE Business School
27. 27. Fin Sesión Cinco