In Exercises 4-6, use critical thinking to address the key issue. 4-Population D
ID: 3203155 • Letter: I
Question
In Exercises 4-6, use critical thinking to address the key issue.
4-Population Data – On Monday, October 31, 2011 the Reuters international news agency ran this front-page headline: “World’s population hits 7 billion.” What is wrong with this headline?
5-Average of Averages – An economist randomly selects 10 wage earners from each of the 50 states. For each state, he finds the average of the annual incomes, and he then adds those 50 values and divides by 50. Is the result likely to be a good estimate of the average (mean) of all wage earners in the United States? Why or why not?
6-Pictograph – Taxes in Newport have doubled over the past 10 years, and a candidate for mayor wants to construct a graph that emphasizes that point. She represents taxes 10 years ago by using a box with a width, length, and height all equal to 1 inch. She then doubles each dimension to show a larger box representing taxes now. What is the volume of the smaller box? What is the volume of the larger box? Does this pictograph correctly depict the relationship between taxes 10 years ago and taxes now?
Explanation / Answer
5-Average of Averages – An economist randomly selects 10 wage earners from each of the 50 states. For each state, he finds the average of the annual incomes, and he then adds those 50 values and divides by 50. Is the result likely to be a good estimate of the average (mean) of all wage earners in the United States? Why or why not?
Here the right technique used and the technique name is Central Limit Theorem.
Central limit theorem states that, for large sample size the distribution of sample mean goes to normal with mean is population mean and standard deviation is population standard deviation divided by square root of sample size.
6-Pictograph – Taxes in Newport have doubled over the past 10 years, and a candidate for mayor wants to construct a graph that emphasizes that point. She represents taxes 10 years ago by using a box with a width, length, and height all equal to 1 inch. She then doubles each dimension to show a larger box representing taxes now. What is the volume of the smaller box? What is the volume of the larger box? Does this pictograph correctly depict the relationship between taxes 10 years ago and taxes now?
The volume of the smaller box is,
V = side3 = 13 = 1
And volume of the larger box is,
V = 23 = 8
No, the pictograph correctly depict the relationship between taxes 10 years ago and taxes now.