STAT 222 Module 8 QA.pdf

# Chapter 10 critical exercise 22 us states this

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Chapter 10 Critical Exercise 22 U.S. states This question is based on the 50 U.S. states. Each state is an observational unit, and the variables listed are measured separately for each of the 50 states. For each of the following pairs of variables, would you expect the correlation to be strong and positive, moderate and positive, weak or very weak, moderate and negative, or strong and negative. 2012 popular vote for Romney and 2012 popular vote for Obama Correlation should be strong and positive: For states with large populations, both vote totals will be large. For states with small populations, both vote totals will be small. Total 2012 popular vote for president and 2012 number of electoral votes Correlation will be positive and very strong. A state's electoral vote total is roughly proportional to its population, so states with large populations will have large numbers of electoral votes, and vice-versa. (In more detail, the number of electoral votes is equal to its number of senators plus number of representatives. Each state has two senators and its number of representatives is

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proportional to its population, so (electoral vote) ≈ 2 + ࠵? × (population size ) , where is a positive constant. Number of McDonald's restaurants and number of attorneys Correlation will be strong and positive, because both numbers are related to population size. States with larger populations will have more attorneys and more McDonald's restaurants. States with smaller populations will have fewer of both. High school graduation rate and percentage of people over 25 with a four-year college degree Correlation will be strong and positive because, as a rule, graduation from high school is a requirement for applying to college. States with high rates of graduation from high school will tend to have higher percentages of college graduates. Year of statehood and number of years as a state Correlation will be strong and negative. In fact the correlation will equal -1 because there is a perfect linear relationship with slope -1:(year of statehood)+(years as a state)=(current year). Year of statehood and longitude (east/west) Correlations will be positive and moderate. The U.S. was settled from east to west, which means that as a rule the year of statehood is earlier (lower) for eastern states and later (higher) for western states. Longitude also increases as you go from east to west in the U.S. Thus both quantitative variables tend to increase together as you go from east to west. Longitude and latitude (north/south) Correlation will be near zero, because there is no systematic relationship between a state's north- south location and its east-west location. Latitude and average annual temperature Correlation will be negative and moderate. As a rule, southern states (lower latitudes) tend to have warmer (larger) average annual temperatures, whereas northern states (higher latitudes) tend to have colder (lower) annual temperatures.
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• Summer '18
• Null hypothesis, Statistical hypothesis testing, Correlation and dependence, Pearson product-moment correlation coefficient

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