AEC380-SA-10.2-Hutson

SECTION 10.2 - Exercises AEC 380 — Agricultural Statistics Instructor: Dr. Jose Lopez Name: Cara Hutson Date: March 27, 2021 Submit your answers to the Short Answers (Part II) via the Exercises SE or SA sub-tab in Section 10.2. II. Short Answers 1) State the requirements that must be satisfied to test a hypothesis regarding a population proportion. (Points: 20) In population proportion regarding testing a hypothesis you must have: 1. The Sample that is obtained by sample random sampling. 2. The Sample is Normally distributed. Noted as: np 0 (1- p 0 )  10. 3. The sample values are independent of each other. Given the sample values fall within the value given by n  0.05 N . 2) Distinguish between p and ^ p . (Points: 20) p is the symbol used for Population Proportion in regarding to testing a hypothesis. ^ p is the symbol used for the sample proportion, also called the best point of estimate. 3) In your own words, what is a population mean? (Points: 10) Provide an example of a population mean. (Points: 10) Make sure it is clear in your example you are referring to a population. Hint: Review the difference between population and sample in Section 1.1. A Population refers to the total observations as a whole, instead of just parts. A Population mean would be the average of the given observations that are presented. For example, given that the observations of the height of the Girls Gymnastics team are 64, 60, 56, 63, 64; the population mean would then be, 61.4. 4) In your own words, what is a population proportion? (Points: 10) Provide an example of a population proportion. (Points: 10) Make sure it is clear in your example you are referring to a population. Hint: Review the difference between population and sample in Section 1.1. The population proportion is the fraction of the population that has a certain characteristic, versus the entire population. An example would be, using the same Girls Gymnastics team from above, for a total of 5 girls, 1 is a Burnette, 3 are Blonde, and 1 is a Red Head. If we are looking for the population proportion of the Blondes in the group we would calculate it by: P=X/N P=3/5 P=0.6 would be our population proportion. 5) The figure below explains how to determine the appropriate hypothesis test to perform. That is, the figure shows which approach to take in testing hypotheses for the two parameters 1

discussed in this chapter: the population mean and the population proportion. Write a paragraph explaining and discussing the figure. (Points: 20) The first question to ask is what the parameter is being used in the formulated question. If the parameter is the proportion, then we move to the equation using all of the given and calculated values thus ending with an equation and reading the answer to Z o , as the sample proportion. If we are given the Mean then we have to ask two questions, is the  given? If yes, then we continue onto the equation given, z o =, with sample size is 30 or above, to calculate the normal distribution. If no, then. We use the second equation, t o =, with a sample size of 30 or above and calculate the t-distribution to determine the degrees of freedom within the hypothesis. 2