STAT 3460 Lecture Notes - Lecture 4: Linear Combination, Random Variable

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mauveelephant396

14 Mar 2016

School

Ohio State University

Department

Statistics

Course

STAT 3460

Professor

Chenggong Han, Laura Kubatko, Min Ho Cho, Yuan Gao

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Document Summary

Adding a constant: if x is a random variable and b is a constant, then x + b = x + b and x + b. Means of linear combinaions of random variables. Independent random variables: if x1, , xn are independent random variables, and s1, , sn are sets, then p(x1. Independence and simple random samples: if x1, , xn is a sample random sample, then they are treated independently with the same distribuion. The mean and variance of a sample mean: if x1, , xn are independent and idenically distributed then x. X is equal to the mean of the distribuion of all the xi"s.

Related Questions

A data set contains information from a random sample of 120 different female dogs who have bred,
40 of which are labradors, 40 are golden retrievers, and 40 are German shepherds.
The variables are:
• Breed: breed of the dog
• LitterSize: the number of pups in the dog’s most recent litter
The data are contained in the file dogs.sav.

(a) [6 marks] Is there evidence of a difference in the population mean litter sizes for the three
breeds? Be sure to state the null and alternative hypotheses, test statistic, null distribution,
p-value, decision, and an appropriate conclusion in plain language.

(b) [3 marks] If appropriate, perform post-hoc tests to determine which breeds have significantly
different mean litter sizes. If post-hoc tests are not appropriate, explain the purpose of a post-hoc
test and why it’s not appropriate in this example.

(c) [2 marks] Report the 95% pairwise confidence interval for the mean difference in litter sizes
between golden retrievers and German shepherds. Interpret this interval with a sentence in plain
language.

(d) [3 marks] What are the assumptions of the analysis performed in part (a)? State whether
each assumption is reasonable with reference to appropriate SPSS output.

scarletlocust45

5. Consider the following class: import java.util.Scanner; public class Money private int dollars; private int cents; public Money (int d, int c) { dollars = d; cents = c; /* Point 1 */ public String toString() { String result; if (cents > 100) int totalCents = dollars * 100 + cents; dollars = totalCents / 100; cents = total Cents % 100; /* Point 2 */ /* Point 3 */ result = "$" + dollars + ", " + cents + "C"; return result; public static void main(String[] yourGrandfather) Scanner keyboard - new Scanner (System.in); Money amount; int C; /* Point 4 */ System.out.print("Enter an amount in cents: "); C = keyboard.nextInt (); amount = new Money (c/ 100, CX 100); System.out.println("You have: " + amount.toString()); The above program compiles and runs without error. Which variables are in scope at each of the points marked by comments in the above class? In other words, if each of these comments were replaced by an actual Java statement, which variables could be used in this statement without a prefix (that is, without having to write the name of a class or other variable in front of the variable name) and without the compiler reporting an unknown variable error? List each variable that is in scope at each of the points marked by comments in the above class, and indicate whether it is an instance variable, a formal parameter, or a local variable. Note that you will be penalized for every variable that is out of scope at a given point but that you list as being in scope at that point.

Researchers measured the blood pressures of 22 students in

two situations: when the students were relaxed and when the students were taking an

important examination. The file

systolic.txt

lists the systolic and diastolic pressures for

each student in each situation. Dataset is available at

systolic_url = "https://mcs.utm.utoronto.ca/~nosedal/data/systolic.txt"

Use R

to answer each of the following questions. You have to show

all your work

to get

full credit.