Below are several induction hypothesis statements. Select all the statements that are using STRONG induction. Note: The assumptions themselves are made up. Assume for all natural numbers k up to and including n, that k can be written as the sum of a prime and even number Assume that n is a perfect number We will suppose that for any k, k can be expressed as the root of a polynomial Suppose all integers up to n are good numbers

UNIVERSITY OF BOTSWANA FACULTY OF SCIENCE DEPARTMENT OF MATHEMATICS MAT271 INTRODUCTION TO MATHEMATICAL STATISTICS TUTORIAL EXECISES 1 PART I. COUNTING PRINCIPLES I (1) A president and a treasurer are to be chosen from a student club consisting of 50 people. How many different choices of officers are possible if (a) there are no restrictions; (b) A will serve only if he is president; (c) B and C will serve together or not at all; (d) D and E will not serve together? (2) Four married couples have bought 8 scats in the same row for a concert. In how many different ways can they be seated (a) With no restrictions? (b) If each couple is to sit together? (c) If all the men sit together to the right of all the women? (3) You are going on a road trip with 4 friends in a car that fits 5 people. How many different ways can everyone sit if you have to drive the whole way? (4) In how many ways can 4 boys and 5 girls sit in a row if the boys and girls must alternate? (5) In how many ways can 5…

When conducting a hypothesis test, the hypothesis that illustrates the initial claim being tested about the population is called the ___________________________, whereas the hypothesis that illustrates what we really think is going on is called the ______________________.   research hypothesis; null hypothesis alternative hypothesis; research hypothesis null hypothesis; alternative hypothesis alternative hypothesis; null hypothesis theoretical hypothesis; realistic hypothesis

Dimensional characteristics, such as height, are an example of a:   a.   continuous random variable   b.   discrete random variable   c.   categorical random variable   d.   Any of the above