Hypothess test computation
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Catégorie :Category: nCreator TI-Nspire
Auteur Author: NSRBIKE
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 4.17 Ko KB
Mis en ligne Uploaded: 24/10/2024 - 07:05:10
Uploadeur Uploader: NSRBIKE (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4272518
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 4.17 Ko KB
Mis en ligne Uploaded: 24/10/2024 - 07:05:10
Uploadeur Uploader: NSRBIKE (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4272518
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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Here is the content of the PDF you uploaded, formatted in a simple text form for you to copy and paste: --- ### **Significance Testing** **HYPOTHESIS TESTING** Accepting or rejecting a hypothesis --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** A call center claims that the average waiting time for customers is at most 90 seconds. You are not so sure of this claim and want to challenge this fact with data. You collect some data by taking a sample of 100 randomly chosen calls. With this information, can you reject the call center claim about customer waiting time? The data evidence that you obtain is the following: - A data sample that seems normal (by its histogram) - Sample mean = 93 seconds - Sample standard deviation = 10 seconds --- ### **Some Facts We Can Deduce/Assume** 1. Because the sample histogram looks normally distributed (at least for a sample of that size), we will assume that the population is normally distributed. 2. Because the population is normally distributed and the sample size is big enough (100 >> 30), we will assume that the sample standard deviation and the population standard deviation are virtually equal. So, à = 10 secs. --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** The call center claims that waiting times are according to the following distribution: - **Normal distribution** - Mean = 90s - Standard deviation = 10s --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** Our sample of size 100 follows the red distribution, which is a bit more to the right. - **Normal-ish distribution** - Mean = 93s - Standard deviation = 10s - **Normal distribution** - Mean = 90s - Standard deviation = 10s This graph is suspicious but does not prove anything!! We need to do our Hypothesis testing work. --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** Rephrased as an hypothesis testing problem: A sample of N=100 is drawn from a population that is normally distributed with a known standard deviation of 10. The sample mean is 93, and the claim to test is that the population mean is 90 or less. - a) Write the Null and Alternative Hypothesis - b) Is it a one-sided or a two-sided test? - c) Can we reject the Null Hypothesis? - d) Should I hire this call center to handle my phone call? --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** The call center claims that waiting times are according to the following distribution and the mean is 90 seconds OR LESS. - **H:** ¼ d 90 - **H:** ¼ > 90 a) Write the Null and Alternative Hypothesis b) Is it a one-sided or a two-sided test? - **One-sided** --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** **Sampling Distribution** - n = 100 - Mean = 90 - SE = à / n = 1 --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** Lets measure the distance from X to ¼ in terms of how many standard errors separate them. Lets call this distance the Z value. Z = (X - ¼) / (à / N) = 3 > 2.326 = z A sample mean of 93 seconds is 3 standard errors to the right of the expected mean. Is that a lot? => It depends on my significance level!! --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** The right question to ask: Is the value Z = 3 in my acceptance region or in my rejection region? 1-sided test: The rejection region is obtained by selecting a confidence level. For ± = 0.01, the critical z = 2.326. --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** - **Acceptance region** - **Rejection region** - z = 2.326, Z = 3 Our value Z is inside the rejection region. We should then reject the Null Hypothesis that the waiting time has an average of 90 seconds! Think twice before hiring that call center. --- ### **Complete Solution: Hypothesis Testing Example** Call center claim: ¼ d 90 seconds, and à = 10 (assume normal distribution). Sample N=100, sample mean = 93 seconds. Should I hire this call center? #### **Step 1: Set Null Hypothesis and Type of Test** - **H:** ¼ d 90 - **H:** ¼ > 90 One-sided test. Reject the hypothesis (dont hire center) if waiting time is clearly > 90. Rejection region to the right. [ Z = frac{X - ¼}{sigma / sqrt{N}} = 3 > 2.326 = z ] **Conclusion:** Reject Null Hypothesis, dont hire that call center. --- #### **Step 2: Fix a Confidence Level** Lets take ± = 0.01 (small number because I want to be confident that I do not commit a Type I error). #### **Step 3: Compute Critical Level** Using Python or memory (this is a common alpha value), z = 2.326. #### **Step 4: Compute the Z-value** --- ### **Useful Critical Values** | **Type of Test** | ± = 0.1 | ± = 0.05 | ± = 0.01 | | ---------------- | ------ | ------- | ------- | | One-sid (right) | 1.282 | 1.654 | 2.326 | | One-sided (left) | -1.282 | -1.654 | -2.326 | | Two-sided | ±1.645 | ±1.96 | ±2.576 | --- Feel free to copy and paste this wherever needed! Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
Here is the content of the PDF you uploaded, formatted in a simple text form for you to copy and paste: --- ### **Significance Testing** **HYPOTHESIS TESTING** Accepting or rejecting a hypothesis --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** A call center claims that the average waiting time for customers is at most 90 seconds. You are not so sure of this claim and want to challenge this fact with data. You collect some data by taking a sample of 100 randomly chosen calls. With this information, can you reject the call center claim about customer waiting time? The data evidence that you obtain is the following: - A data sample that seems normal (by its histogram) - Sample mean = 93 seconds - Sample standard deviation = 10 seconds --- ### **Some Facts We Can Deduce/Assume** 1. Because the sample histogram looks normally distributed (at least for a sample of that size), we will assume that the population is normally distributed. 2. Because the population is normally distributed and the sample size is big enough (100 >> 30), we will assume that the sample standard deviation and the population standard deviation are virtually equal. So, à = 10 secs. --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** The call center claims that waiting times are according to the following distribution: - **Normal distribution** - Mean = 90s - Standard deviation = 10s --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** Our sample of size 100 follows the red distribution, which is a bit more to the right. - **Normal-ish distribution** - Mean = 93s - Standard deviation = 10s - **Normal distribution** - Mean = 90s - Standard deviation = 10s This graph is suspicious but does not prove anything!! We need to do our Hypothesis testing work. --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** Rephrased as an hypothesis testing problem: A sample of N=100 is drawn from a population that is normally distributed with a known standard deviation of 10. The sample mean is 93, and the claim to test is that the population mean is 90 or less. - a) Write the Null and Alternative Hypothesis - b) Is it a one-sided or a two-sided test? - c) Can we reject the Null Hypothesis? - d) Should I hire this call center to handle my phone call? --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** The call center claims that waiting times are according to the following distribution and the mean is 90 seconds OR LESS. - **H:** ¼ d 90 - **H:** ¼ > 90 a) Write the Null and Alternative Hypothesis b) Is it a one-sided or a two-sided test? - **One-sided** --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** **Sampling Distribution** - n = 100 - Mean = 90 - SE = à / n = 1 --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** Lets measure the distance from X to ¼ in terms of how many standard errors separate them. Lets call this distance the Z value. Z = (X - ¼) / (à / N) = 3 > 2.326 = z A sample mean of 93 seconds is 3 standard errors to the right of the expected mean. Is that a lot? => It depends on my significance level!! --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** The right question to ask: Is the value Z = 3 in my acceptance region or in my rejection region? 1-sided test: The rejection region is obtained by selecting a confidence level. For ± = 0.01, the critical z = 2.326. --- ### **HYPOTHESIS TESTING: WORKING EXAMPLE** - **Acceptance region** - **Rejection region** - z = 2.326, Z = 3 Our value Z is inside the rejection region. We should then reject the Null Hypothesis that the waiting time has an average of 90 seconds! Think twice before hiring that call center. --- ### **Complete Solution: Hypothesis Testing Example** Call center claim: ¼ d 90 seconds, and à = 10 (assume normal distribution). Sample N=100, sample mean = 93 seconds. Should I hire this call center? #### **Step 1: Set Null Hypothesis and Type of Test** - **H:** ¼ d 90 - **H:** ¼ > 90 One-sided test. Reject the hypothesis (dont hire center) if waiting time is clearly > 90. Rejection region to the right. [ Z = frac{X - ¼}{sigma / sqrt{N}} = 3 > 2.326 = z ] **Conclusion:** Reject Null Hypothesis, dont hire that call center. --- #### **Step 2: Fix a Confidence Level** Lets take ± = 0.01 (small number because I want to be confident that I do not commit a Type I error). #### **Step 3: Compute Critical Level** Using Python or memory (this is a common alpha value), z = 2.326. #### **Step 4: Compute the Z-value** --- ### **Useful Critical Values** | **Type of Test** | ± = 0.1 | ± = 0.05 | ± = 0.01 | | ---------------- | ------ | ------- | ------- | | One-sid (right) | 1.282 | 1.654 | 2.326 | | One-sided (left) | -1.282 | -1.654 | -2.326 | | Two-sided | ±1.645 | ±1.96 | ±2.576 | --- Feel free to copy and paste this wherever needed! Made with nCreator - tiplanet.org
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