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Question setup: In the first question in this series of questions, you were presented with 3 scenarios. The scenarios were: - Scenario 1: you collect a sample of n=3, and obtain p - Scenario 2: you collect a sample of n=6, and obtain p = = - Scenario 3: you collect a sample of n=300, and obtain p = Question: use the dropdowns to select the correct answers: The sample sizes for Scenarios 1 and 2 are not sufficient to approach approximate normality, so we cannot use the test statistics that we are familiar with in these scenarios. However, if we understand the basic principle behind hypothesis testing as seeing how likely/unlikely a sample statistic is under the null hypothesis, we can come up with other reasonable ways to test our hypothesis. To do this, we need to figure out a sample statistic and its distribution under the null hypothesis. #successes # trials is not great at such small samples and its distribution is harder to figure out. What if we didn't divide by # trials? We know that: 1) Our data is categorical (success/failure) 2) Under the null hypothesis, the probability that a randomly selected person failed the course is 1/2. 3) One unspoken assumption we have been making is that the observations in our data are independent. Thus, assuming the null hypothesis proportion of 1/2, the number of people in a random sample of size n who failed the course should follow a Binomial(n, 1/2) We now have a sampling distribution for a sample statistic (the number of "successes" in our sample of size n), and can use this to compute a p-value for a two-sided test for Scenarios 1&2: The p-value for Scenario 1 is exactly 1. (yes, really! This should make sense if you consider the possible values of the sample statistic) And the p-value for Scenario 2 is 2*pbinom(2, size=6, prob=0.5

Question setup: In the first question in this series of questions, you were presented with 3 scenarios. The scenarios were: - Scenario 1: you collect a sample of n=3, and obtain p - Scenario 2: you collect a sample of n=6, and obtain p = = - Scenario 3: you collect a sample of n=300, and obtain p = Question: use the dropdowns to select the correct answers: The sample sizes for Scenarios 1 and 2 are not sufficient to approach approximate normality, so we cannot use the test statistics that we are familiar with in these scenarios. However, if we understand the basic principle behind hypothesis testing as seeing how likely/unlikely a sample statistic is under the null hypothesis, we can come up with other reasonable ways to test our hypothesis. To do this, we need to figure out a sample statistic and its distribution under the null hypothesis. #successes # trials is not great at such small samples and its distribution is harder to figure out. What if we didn't divide by # trials? We know that: 1) Our data is categorical (success/failure) 2) Under the null hypothesis, the probability that a randomly selected person failed the course is 1/2. 3) One unspoken assumption we have been making is that the observations in our data are independent. Thus, assuming the null hypothesis proportion of 1/2, the number of people in a random sample of size n who failed the course should follow a Binomial(n, 1/2) We now have a sampling distribution for a sample statistic (the number of "successes" in our sample of size n), and can use this to compute a p-value for a two-sided test for Scenarios 1&2: The p-value for Scenario 1 is exactly 1. (yes, really! This should make sense if you consider the possible values of the sample statistic) And the p-value for Scenario 2 is 2*pbinom(2, size=6, prob=0.5

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question setup: In the first question in this series of questions, you were presented with 3 scenarios. The scenarios were: - Scenario 1: you collect a sample of n=3, and obtain p - Scenario 2: you collect a sample of n=6, and obtain p = = - Scenario 3: you collect a sample of n=300, and obtain p = Question: use the dropdowns to select the correct answers: The sample sizes for Scenarios 1 and 2 are not sufficient to approach approximate normality, so we cannot use the test statistics that we are familiar with in these scenarios. However, if we understand the basic principle behind hypothesis testing as seeing how likely/unlikely a sample statistic is under the null hypothesis, we can come up with other reasonable ways to test our hypothesis. To do this, we need to figure out a sample statistic and its distribution under the null hypothesis. #successes # trials is not great at such small samples and its distribution is harder to figure out. What if we didn't divide by # trials? We know that: 1) Our data is categorical (success/failure) 2) Under the null hypothesis, the probability that a randomly selected person failed the course is 1/2. 3) One unspoken assumption we have been making is that the observations in our data are independent. Thus, assuming the null hypothesis proportion of 1/2, the number of people in a random sample of size n who failed the course should follow a Binomial(n, 1/2) We now have a sampling distribution for a sample statistic (the number of "successes" in our sample of size n), and can use this to compute a p-value for a two-sided test for Scenarios 1&2: The p-value for Scenario 1 is exactly 1. (yes, really! This should make sense if you consider the possible values of the sample statistic) And the p-value for Scenario 2 is 2*pbinom(2, size=6, prob=0.5
Transcribed Image Text:Question setup: In the first question in this series of questions, you were presented with 3 scenarios. The scenarios were: - Scenario 1: you collect a sample of n=3, and obtain p - Scenario 2: you collect a sample of n=6, and obtain p = = - Scenario 3: you collect a sample of n=300, and obtain p = Question: use the dropdowns to select the correct answers: The sample sizes for Scenarios 1 and 2 are not sufficient to approach approximate normality, so we cannot use the test statistics that we are familiar with in these scenarios. However, if we understand the basic principle behind hypothesis testing as seeing how likely/unlikely a sample statistic is under the null hypothesis, we can come up with other reasonable ways to test our hypothesis. To do this, we need to figure out a sample statistic and its distribution under the null hypothesis. #successes # trials is not great at such small samples and its distribution is harder to figure out. What if we didn't divide by # trials? We know that: 1) Our data is categorical (success/failure) 2) Under the null hypothesis, the probability that a randomly selected person failed the course is 1/2. 3) One unspoken assumption we have been making is that the observations in our data are independent. Thus, assuming the null hypothesis proportion of 1/2, the number of people in a random sample of size n who failed the course should follow a Binomial(n, 1/2) We now have a sampling distribution for a sample statistic (the number of "successes" in our sample of size n), and can use this to compute a p-value for a two-sided test for Scenarios 1&2: The p-value for Scenario 1 is exactly 1. (yes, really! This should make sense if you consider the possible values of the sample statistic) And the p-value for Scenario 2 is 2*pbinom(2, size=6, prob=0.5
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