Statistics math questions

Question

1. A political researcher wishes to gauge political sentiment regarding a proposed tax cut. He obtains a list of 1000 email addresses from an internet provider, uses a random number table and collects a random sample of 100 of these addresses, emails the people in the sample and requests that they responds to his questions by email. Do you think that the group of people who respond is likely to be representative of all registered voters? Explain your answer. Suppose you are comparing frequency data for two different groups, 25 managers and 150 blue collar workers. Why would a relative frequency distribution be better than a frequency distribution? A frequency distribution with the following classes was set up. Number Frequency 0-3 3-6 6-9 9-12 What is wrong with these classes. Describe a way the classes could have been correctly depicted.

2. A survey is being conducted of students’ residences. Data is gathered from a random sample of 1000 students. The data is summarized in the table below. Gender and Residence of Students Males Females Apartment off campus 50 90 Dorm room 150 210 With Parent(s) 100 50 Sorority/ Fraternity House 200 150 a) What is the probability that a student is female and lives in a dorm? ____________________ b) What is the probability that a student is female given that she lives in a dorm?

Answer 1

For Question 1: Only selecting from a list of email from a specific internet provider limits the people that you might be in your sample (maybe older people don't have an email also who the internet provider is could skew your sample towards or away from certain groups...AOL is not used by many people anymore). Also sending an email and asking for a response (Voluntary) can give you biased answers, often only people with complaints reply to such requests, so you would not necessarily get a true representative set of responses.

When the size of your data set differ so much 25 vs. 150 a frequency distribution won't allow for a meaningful comparison of the 2 groups, by turning to relative frequency you will be using percentages which don't get skewed by the size of the group.

For Question 2 the numerator is the single cell where the row and column for Female and Live in a Dorm intersect. The denominator is the total number of student that live in a dorm