Go - Graded Week 6 Homework-Mark Kasule

Student: Mark Kasule Date: 03/26/24 Instructor: Petal Sumner Course: STAT 200 6961 Introduction to Statistics (1) Assignment: Go - Graded Week 6 Homework A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights (in centimeters) of randomly selected presidents along with the heights of their main opponents. Complete parts (a) and (b) below. Height (cm) of President 195 189 188 193 182 185 Height (cm) of Main Opponent 191 193 184 185 200 181 a. Use the sample data with a significance level to test the claim that for the population of heights for presidents and their main opponents, the differences have a mean greater than 0 cm. 0.05 Begin by checking the requirements for inference. The first requirement is that the sample data are dependent, that is, they are matched pairs. The pairs of values are matched by election years, so the sample data are dependent. Next, check that the matched pairs are a random sample. It is given that the presidents are randomly selected, so this requirement is satisfied. Now, check the requirement that either the number of pairs of sample data is large (n 30) or the pairs of values have differences that are from a population having a distribution that is approximately normal. > Since there are n 6 pairs, check the requirement that the differences are from a population having a distribution that is approximately normal. A normal quantile plot of the differences is shown on the right. = Based on the normal quantile plot, the points approximate a straight-line pattern and there are no outliers. -20 -10 0 10 20 30 -2 -1 0 1 2 X Values z score Thus, the differences satisfy the normality requirement. To identify the null and alternative hypotheses, first identify the specific claim or hypothesis to be tested, and put it in symbolic form. In this example, is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the president's height minus their main opponent's height. The claim is that for the population of heights for presidents and their main opponents, the differences have a mean greater than 0 cm. This is expressed in symbolic form as 0 cm. μ d μ d > If 0 cm is false, then 0 cm is true. μ d > μ d ≤ Because the claim of 0 cm does not contain equality, it becomes the alternative hypothesis. μ d > The null hypothesis must express equality. The correct null and alternative hypotheses are given below. : 0 cm H 0 μ d = : 0 cm H 1 μ d > The formula for the test statistic for dependent samples is given below, where and are the mean value and standard deviation, respectively, of the differences d for the paired sample data, is the mean value of the differences d for the population of all pairs of data, d is an individual difference between the two values in a single matched pair, and n is the number of pairs of data. d s d μ d t , , = d − μ d s d n s d = n ∑ d 2 − ∑ d 2 n( ) n − 1 d = ∑ d n The hypothesis test can be conducted using technology or using formulas and tables. For the purposes of this exercise, use technology. Input the data into technology and read the value of the test statistic t from a technology output, rounding to two decimal places. t = − 0.09 The P-value is the probability of getting a value of the test statistic that is at least as extreme as the one representing the sample data, Go - Graded Week 6 Homework-Mark Kasule https://tdx.acs.pearsonprd.tech/api/v1/print/highered 1 of 2 3/26/24, 8:07 PM