Introductory Statistics

# Bringing It Together: Homework

Introductory StatisticsBringing It Together: Homework

78.

The average number of people in a family that attended college for various years is given in Table 12.29.

Year Number of Family Members Attending College
1969 4.0
1973 3.6
1975 3.2
1979 3.0
1983 3.0
1988 3.0
1991 2.9
Table 12.29
1. Using “year” as the independent variable and “Number of Family Members Attending College” as the dependent variable, draw a scatter plot of the data.
2. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx
3. Find the correlation coefficient. Is it significant?
4. Pick two years between 1969 and 1991 and find the estimated number of family members attending college.
5. Based on the data in Table 12.29, is there a linear relationship between the year and the average number of family members attending college?
6. Using the least-squares line, estimate the number of family members attending college for 1960 and 1995. Does the least-squares line give an accurate estimate for those years? Explain why or why not.
7. Are there any outliers in the data?
8. What is the estimated average number of family members attending college for 1986? Does the least squares line give an accurate estimate for that year? Explain why or why not.
9. What is the slope of the least squares (best-fit) line? Interpret the slope.
79.

The percent of female wage and salary workers who are paid hourly rates is given in Table 12.30 for the years 1979 to 1992.

Year Percent of workers paid hourly rates
1979 61.2
1980 60.7
1981 61.3
1982 61.3
1983 61.8
1984 61.7
1985 61.8
1986 62.0
1987 62.7
1990 62.8
1992 62.9
Table 12.30
1. Using “year” as the independent variable and “percent” as the dependent variable, draw a scatter plot of the data.
2. Does it appear from inspection that there is a relationship between the variables? Why or why not?
3. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx
4. Find the correlation coefficient. Is it significant?
5. Find the estimated percents for 1991 and 1988.
6. Based on the data, is there a linear relationship between the year and the percent of female wage and salary earners who are paid hourly rates?
7. Are there any outliers in the data?
8. What is the estimated percent for the year 2050? Does the least-squares line give an accurate estimate for that year? Explain why or why not.
9. What is the slope of the least-squares (best-fit) line? Interpret the slope.

Use the following information to answer the next two exercises. The cost of a leading liquid laundry detergent in different sizes is given in Table 12.31.

Size (ounces) Cost ($) Cost per ounce 16 3.99 32 4.99 64 5.99 200 10.99 Table 12.31 80. 1. Using “size” as the independent variable and “cost” as the dependent variable, draw a scatter plot. 2. Does it appear from inspection that there is a relationship between the variables? Why or why not? 3. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx 4. Find the correlation coefficient. Is it significant? 5. If the laundry detergent were sold in a 40-ounce size, find the estimated cost. 6. If the laundry detergent were sold in a 90-ounce size, find the estimated cost. 7. Does it appear that a line is the best way to fit the data? Why or why not? 8. Are there any outliers in the given data? 9. Is the least-squares line valid for predicting what a 300-ounce size of the laundry detergent would you cost? Why or why not? 10. What is the slope of the least-squares (best-fit) line? Interpret the slope. 81. 1. Complete Table 12.31 for the cost per ounce of the different sizes. 2. Using “size” as the independent variable and “cost per ounce” as the dependent variable, draw a scatter plot of the data. 3. Does it appear from inspection that there is a relationship between the variables? Why or why not? 4. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx 5. Find the correlation coefficient. Is it significant? 6. If the laundry detergent were sold in a 40-ounce size, find the estimated cost per ounce. 7. If the laundry detergent were sold in a 90-ounce size, find the estimated cost per ounce. 8. Does it appear that a line is the best way to fit the data? Why or why not? 9. Are there any outliers in the the data? 10. Is the least-squares line valid for predicting what a 300-ounce size of the laundry detergent would cost per ounce? Why or why not? 11. What is the slope of the least-squares (best-fit) line? Interpret the slope. 82. According to a flyer by a Prudential Insurance Company representative, the costs of approximate probate fees and taxes for selected net taxable estates are as follows: Net Taxable Estate ($) Approximate Probate Fees and Taxes ($) 600,000 30,000 750,000 92,500 1,000,000 203,000 1,500,000 438,000 2,000,000 688,000 2,500,000 1,037,000 3,000,000 1,350,000 Table 12.32 1. Decide which variable should be the independent variable and which should be the dependent variable. 2. Draw a scatter plot of the data. 3. Does it appear from inspection that there is a relationship between the variables? Why or why not? 4. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx. 5. Find the correlation coefficient. Is it significant? 6. Find the estimated total cost for a next taxable estate of$1,000,000. Find the cost for $2,500,000. 7. Does it appear that a line is the best way to fit the data? Why or why not? 8. Are there any outliers in the data? 9. Based on these results, what would be the probate fees and taxes for an estate that does not have any assets? 10. What is the slope of the least-squares (best-fit) line? Interpret the slope. 83. The following are advertised sale prices of color televisions at Anderson’s. Size (inches) Sale Price ($)
9 147
20 197
27 297
31 447
35 1177
40 2177
60 2497
Table 12.33
1. Decide which variable should be the independent variable and which should be the dependent variable.
2. Draw a scatter plot of the data.
3. Does it appear from inspection that there is a relationship between the variables? Why or why not?
4. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx
5. Find the correlation coefficient. Is it significant?
6. Find the estimated sale price for a 32 inch television. Find the cost for a 50 inch television.
7. Does it appear that a line is the best way to fit the data? Why or why not?
8. Are there any outliers in the data?
9. What is the slope of the least-squares (best-fit) line? Interpret the slope.
84.

Table 12.34 shows the average heights for American boy s in 1990.

Age (years) Height (cm)
birth 50.8
2 83.8
3 91.4
5 106.6
7 119.3
10 137.1
14 157.5
Table 12.34
1. Decide which variable should be the independent variable and which should be the dependent variable.
2. Draw a scatter plot of the data.
3. Does it appear from inspection that there is a relationship between the variables? Why or why not?
4. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx
5. Find the correlation coefficient. Is it significant?
6. Find the estimated average height for a one-year-old. Find the estimated average height for an eleven-year-old.
7. Does it appear that a line is the best way to fit the data? Why or why not?
8. Are there any outliers in the data?
9. Use the least squares line to estimate the average height for a sixty-two-year-old man. Do you think that your answer is reasonable? Why or why not?
10. What is the slope of the least-squares (best-fit) line? Interpret the slope.
85.
State # letters in name Year entered the Union Ranks for entering the Union Area (square miles)
Alabama 7 1819 22 52,423
Hawaii 6 1959 50 10,932
Iowa 4 1846 29 56,276
Maryland 8 1788 7 12,407
Missouri 8 1821 24 69,709
New Jersey 9 1787 3 8,722
Ohio 4 1803 17 44,828
South Carolina 13 1788 8 32,008
Utah 4 1896 45 84,904
Wisconsin 9 1848 30 65,499
Table 12.35

We are interested in whether there is a relationship between the ranking of a state and the area of the state.

1. What are the independent and dependent variables?
2. What do you think the scatter plot will look like? Make a scatter plot of the data.
3. Does it appear from inspection that there is a relationship between the variables? Why or why not?
4. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx
5. Find the correlation coefficient. What does it imply about the significance of the relationship?
6. Find the estimated areas for Alabama and for Colorado. Are they close to the actual areas?
7. Use the two points in part f to plot the least-squares line on your graph from part b.
8. Does it appear that a line is the best way to fit the data? Why or why not?
9. Are there any outliers?
10. Use the least squares line to estimate the area of a new state that enters the Union. Can the least-squares line be used to predict it? Why or why not?
11. Delete “Hawaii” and substitute “Alaska” for it. Alaska is the forty-ninth, state with an area of 656,424 square miles.
12. Calculate the new least-squares line.
13. Find the estimated area for Alabama. Is it closer to the actual area with this new least-squares line or with the previous one that included Hawaii? Why do you think that’s the case?
14. Do you think that, in general, newer states are larger than the original states?
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