UG-BNAN-276-Written-Assignment-Chapter-7 Charles Copeland (1)

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Feb 20, 2024

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Statistical Inference in Management Week 5: Written Assignment Chapter 7 Charles Copeland Written Assignment Chapter 7 1. How are a sample and a population related? - A population is the qualities of the group that you, as a researcher, want to investigate and question. You cannot obtain all of a population's observations due to time constraints, limited resources, and other factors. Instead, you choose observations at random from the population to create a sample. You may then utilize the sample to form inferences, or statements about the population. 2. What are parameters associated with? - Unknown and Constant. 3. What are the 3 parameters displayed/discussed in lecture? (note: parameters are Greek letters) - Sigma, mu, ro(p). 4. What are statistics associated with? - Statistics are measurements of a sample . 5. What are the 3 statistics displayed/discussed in lecture? - Sample mean "x-bar", sample standard deviation "s", and sample percentage "p- bar.” 6. What is the purpose of a statistic ? - Making assumptions about the population based on estimations. Estimates are just the statistics of a sample. 7. What is consistency ? - A statistic's value should approach that of the population parameter as the number of observations (n) in a sample increase. 8. What is bias ? - Overestimate or underestimate of any parameter by a statistic. 9. What can be done to help eliminate bias from a sample? - Designing your observations properly. 10. What are the three sample designs discussed in the lecture? - Simple, Stratified, Cluster. 11. What are some examples of simple random sampling ? - The number generator, tossing a dice, choosing names out of a hat. 12. What are the two steps of stratified random sampling ? - The first step is to group, and the second step is to randomly choose a proportionate number of observations from each group to create your sample. 13. What are the two steps of cluster random sampling ? - The initial stage is to group, followed by selecting some of the groupings at random. 14. Which of the three designs is the most sophisticated? - Stratified.
Page 2 of 3 Copyright © Arizona Board of Regents 15. Which of the three designs can produce a large amount of bias if you are not careful in how you design it? - Cluster. 16. How does a sampling distribution of sample means come about? Understand the student debt example from class. - 1) Define your population, and 2) randomly choose observations to obtain a first sample and a first-sample mean. Repeat step 2 to get a large number of sample means. The sample mean is represented by a number. The sample means will differ. Plot the means in a histogram to generate the distribution . 17. If a population distribution is normally distributed, what does that mean for the sampling distribution of sample means ? - It will likewise be typical, regardless of how many sample means you have . 18. Use the Sampling Distribution simulator as instructed here , and copy/paste your results into document. 19. What if a population distribution is not normal - How can we get it so we can assume normality for the sampling distribution of sample means ? - If the total amount of samples, or sample means, hits a predetermined threshold (30) . 20. What is the Central Limit Theorem ? - If the total number of samples, i.e. sample means, reaches a particular number (30), we may conclude the sampling distribution of sample means is normal, independent of the population distribution from which it originated . 21. How is the Central Limit Theorem shown with the simulator as instructed here ? 22. Why does dispersion matter? Understand example of throwing darts. - Comprehend instance of tossing darts. The less scattering in an example the more noteworthy the assessing force of the example measurement. 23. Why does sample size matter? Understand example of throwing darts. - The sample statistic's estimating power improves as the number of observations in the sample increases. 24. Where is the standard error located in the z-score formula? - Whole denominator. 25. How does the sample size ( n ) affect the standard error? (Remember standard error is just a measure of dispersion) - As the sample size (n) grows, the standard error reduces. This creates a stronger sample statistic for estimation. 26. Data shows that annual expenditures for Internet-related services per customer was $945 in 2019. Let the population standard deviation of annual expenditure be $170. 1. What is the probability that the average annual expenditure of 10 Internet-related customers in 2019 was less than $870?
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