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There are many measurements of the human body that are positively correlated. For example, the length of one’s forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because, as one measurement increases, so does the other measurement.

You will discover through this project whether a human’s arm span (measured across the body with the arms extended) is correlated to his height.

You will need to collect data from 11 people, which will give you 12 data points including your own personal data. You will turn in and answer questions regarding only one scatter plot if doing the project alone.

Part One: Measurements

  1. Measure your own height and arm span (from finger-tip to finger-tip) in inches. You will likely need some help from a parent, guardian, or sibling to get accurate measurements. Record your measurements on the “Data Record” document. Use the “Data Record” to help you complete Part Two of this project.
  2. Measure eleven additional people, and record their arm spans and heights in inches.

Part Two: Representing Data with Plots

  1. Using GeoGebra or graphing software of your choice, create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph. Then, use the software to make a box plot.

    Note: Directions for downloading and using GeoGebra can be found in the “Course Information area.”

  2. Copy and paste your scatter plot and box plot into a word processing document.

Part Three: The Line of Best Fit

Include your scatter plot, box plot, and the answers to the following questions in your word processing document, and submit to your instructor. Be sure to review how to save your files before getting started.

  1. Which variable did you plot on the x-axis, and which variable did you plot on the y-axis? Explain why you assigned the variables in that way.
  2. Which two points did you use to draw the line of best fit?
  3. Write the equation of the line passing through those two points using the point-slope formula y−y1=m(x−x1). Show all of your work. Remember to find the slope of the line first.
  4. What does the slope of the line represent within the context of your graph? What does the y-intercept represent?
  5. Test the residuals of two other points to determine how well the line of best fit models the data.
  6. Use the line of best fit to help you to describe the data correlation.
  7. Using the line of best fit that you found in Part 3, Question 3, approximate how tall is a person whose arm span is 66 inches?
  8. According to your line of best fit, what is the arm span of a 74-inch-tall person?
  9. What might cause the arm span and height not to be equal?
  10. Explain why the equation you wrote to represent a human’s arm span (measured across the body with the arms extended) is a correlation and not causation.
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July 1, 2023
    
  1. The Times per week a student uses a lab computer are normally distributed, with a mean of 6.6 hours and a standard deviation of 1.1 hours.  A student is randomly selected. Find the following probabilites

 

  a) Find the probability that a student uses a lab computer less than 4 hours per week is

b ) The probabilty that student uses a lab computer between 5 to 7 hours per week is

c) The probability that a student uses a lab computer more than 8 hours per week is

All answers round to 3 decimal places

  1. A researcher wishes to estimate with 95% confidence. The proportion of adults who have high speed internet. Her estimate must be 1% of the true proportion.
    Find the minimum sample size needed using a prior study that found 34% of the respondents saying they have high speed internet. Then find the minimal sample size for no preliminary estimates available
  2. A random sample of forty-two 200-meter swims has a meant time of 3.724 minutes and a standard deviation of 0.080 minutes. A 95% confidence interval for the population mean time is (3.704,3.744)

Construct a 95% confidence interval for the population mean time using a standard deviation of 0.05 minutes. Which confidence interval is wider?

  1. The state test scores for 12 randomly selected high school seniors are shown below

Assume the population is normally distributed.

 

1428       1220       990        

698         729         831        

730         749         546        

 

(a)    Find the sample mean

(b)   Find the sample standard deviation.

(c)    construct a 99% confidence interval for the population mean u

5.  Assume the Poison distribution applies use the given mean to find the indicated probability.

Find P(4) when u=8

6..

Find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (the pair of variables has a significant correlation) then us the regression equation to predict the value of y for each of the given x-values, if meaningful. The table shoes shoe size and height in inches for 6 men.

 

Shoe size, x

Height, y

6.0

65.5

10.0

70.5

11.0

72.5

11.5

74.5

12.0

74.5

13.0

72.5

 

What is the regression equation?

Predict the value of y for x = 9.5

Predict the value of y for x = 8.0?

Predict the value of y for x = 14.5?

Predict the value of y for x = 9.0 ?

7.  For your study on the food consumption habits of teenage males you randomly select 10 teenage males and aske each how many 12 ounch servings soda he drinks each day. The results are below. At a=0.01, is there enough evidence to support the claim that teenage males drink fewer than three 12ounce servings of soda per day? Assume the population is normally distributed?

3.4

2.9

2.6

2.1

1.9

3.9

2.6

3.6

3.5

1.2

Write the claim mathematically and identify Ho and Ha ?

Use technology to find the P-value

Decide whether to reject or fail to reject the null hypothesis?

Interpret the decision in the context of the original claim.

8. An employment information service claims the mean annual pay for the full-time male workers over age 25 without a high school diploma is $22,350. The annual pay for a random sample of 10 full-time workers over age 25 without a high school diploma is listed. At a=0.10, test the claim that the mean salary is $22,350. Assume the population is normally distributed.

20,650

21,135

22,355

21,399

22,974

16,914

19,150

23,194

24,187

26,287

 

Write the claim mathematically and identify Ho and Ha ?

Find the critical value and identify the rejection region?

Find the standardized test statistic.

Decide whether to reject or fail to reject the null hypothesis?

Interpret the decision in the context of the original claim.?

9. A company that makes cola drinks states that the mean caffeine content per 12-ounch bottle of cola is 50milligrams. You want to test this claim. During your test you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 49.3 milligrams with a standard deviation of 6.6 milligrams. At a=0.02, can you reject the companys claim?

 

Write the claim mathematically and identify Ho and Ha ?

Find the critical value and identify the rejection region?

Decide whether to reject or fail to reject the null hypothesis?

10. The altitude (in thousands of feet) and speed of a plane(in feet per second) for various altitudes is shown below.

Altitude, x

Speed, y

0

962.2

5

1106.8

10

981.8

15

1016.8

20

994.7

25

1007.8

30

1033.1

35

1104.9

The correlation is strong or weak  AND positive or  negative linear correlation?

 

default image
July 1, 2023
    
  1. The Times per week a student uses a lab computer are normally distributed, with a mean of 6.6 hours and a standard deviation of 1.1 hours.  A student is randomly selected. Find the following probabilites

 

  a) Find the probability that a student uses a lab computer less than 4 hours per week is

b ) The probabilty that student uses a lab computer between 5 to 7 hours per week is

c) The probability that a student uses a lab computer more than 8 hours per week is

All answers round to 3 decimal places

  1. A researcher wishes to estimate with 95% confidence. The proportion of adults who have high speed internet. Her estimate must be 1% of the true proportion.
    Find the minimum sample size needed using a prior study that found 34% of the respondents saying they have high speed internet. Then find the minimal sample size for no preliminary estimates available
  2. A random sample of forty-two 200-meter swims has a meant time of 3.724 minutes and a standard deviation of 0.080 minutes. A 95% confidence interval for the population mean time is (3.704,3.744)

Construct a 95% confidence interval for the population mean time using a standard deviation of 0.05 minutes. Which confidence interval is wider?

  1. The state test scores for 12 randomly selected high school seniors are shown below

Assume the population is normally distributed.

 

1428       1220       990        

698         729         831        

730         749         546        

 

(a)    Find the sample mean

(b)   Find the sample standard deviation.

(c)    construct a 99% confidence interval for the population mean u

5.  Assume the Poison distribution applies use the given mean to find the indicated probability.

Find P(4) when u=8

6..

Find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (the pair of variables has a significant correlation) then us the regression equation to predict the value of y for each of the given x-values, if meaningful. The table shoes shoe size and height in inches for 6 men.

 

Shoe size, x

Height, y

6.0

65.5

10.0

70.5

11.0

72.5

11.5

74.5

12.0

74.5

13.0

72.5

 

What is the regression equation?

Predict the value of y for x = 9.5

Predict the value of y for x = 8.0?

Predict the value of y for x = 14.5?

Predict the value of y for x = 9.0 ?

7.  For your study on the food consumption habits of teenage males you randomly select 10 teenage males and aske each how many 12 ounch servings soda he drinks each day. The results are below. At a=0.01, is there enough evidence to support the claim that teenage males drink fewer than three 12ounce servings of soda per day? Assume the population is normally distributed?

3.4

2.9

2.6

2.1

1.9

3.9

2.6

3.6

3.5

1.2

Write the claim mathematically and identify Ho and Ha ?

Use technology to find the P-value

Decide whether to reject or fail to reject the null hypothesis?

Interpret the decision in the context of the original claim.

8. An employment information service claims the mean annual pay for the full-time male workers over age 25 without a high school diploma is $22,350. The annual pay for a random sample of 10 full-time workers over age 25 without a high school diploma is listed. At a=0.10, test the claim that the mean salary is $22,350. Assume the population is normally distributed.

20,650

21,135

22,355

21,399

22,974

16,914

19,150

23,194

24,187

26,287

 

Write the claim mathematically and identify Ho and Ha ?

Find the critical value and identify the rejection region?

Find the standardized test statistic.

Decide whether to reject or fail to reject the null hypothesis?

Interpret the decision in the context of the original claim.?

9. A company that makes cola drinks states that the mean caffeine content per 12-ounch bottle of cola is 50milligrams. You want to test this claim. During your test you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 49.3 milligrams with a standard deviation of 6.6 milligrams. At a=0.02, can you reject the companys claim?

 

Write the claim mathematically and identify Ho and Ha ?

Find the critical value and identify the rejection region?

Decide whether to reject or fail to reject the null hypothesis?

10. The altitude (in thousands of feet) and speed of a plane(in feet per second) for various altitudes is shown below.

Altitude, x

Speed, y

0

962.2

5

1106.8

10

981.8

15

1016.8

20

994.7

25

1007.8

30

1033.1

35

1104.9

The correlation is strong or weak  AND positive or  negative linear correlation?

 

default image
July 1, 2023
    
  1. The Times per week a student uses a lab computer are normally distributed, with a mean of 6.6 hours and a standard deviation of 1.1 hours.  A student is randomly selected. Find the following probabilites

 

  a) Find the probability that a student uses a lab computer less than 4 hours per week is

b ) The probabilty that student uses a lab computer between 5 to 7 hours per week is

c) The probability that a student uses a lab computer more than 8 hours per week is

All answers round to 3 decimal places

  1. A researcher wishes to estimate with 95% confidence. The proportion of adults who have high speed internet. Her estimate must be 1% of the true proportion.
    Find the minimum sample size needed using a prior study that found 34% of the respondents saying they have high speed internet. Then find the minimal sample size for no preliminary estimates available
  2. A random sample of forty-two 200-meter swims has a meant time of 3.724 minutes and a standard deviation of 0.080 minutes. A 95% confidence interval for the population mean time is (3.704,3.744)

Construct a 95% confidence interval for the population mean time using a standard deviation of 0.05 minutes. Which confidence interval is wider?

  1. The state test scores for 12 randomly selected high school seniors are shown below

Assume the population is normally distributed.

 

1428       1220       990        

698         729         831        

730         749         546        

 

(a)    Find the sample mean

(b)   Find the sample standard deviation.

(c)    construct a 99% confidence interval for the population mean u

5.  Assume the Poison distribution applies use the given mean to find the indicated probability.

Find P(4) when u=8

6..

Find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (the pair of variables has a significant correlation) then us the regression equation to predict the value of y for each of the given x-values, if meaningful. The table shoes shoe size and height in inches for 6 men.

 

Shoe size, x

Height, y

6.0

65.5

10.0

70.5

11.0

72.5

11.5

74.5

12.0

74.5

13.0

72.5

 

What is the regression equation?

Predict the value of y for x = 9.5

Predict the value of y for x = 8.0?

Predict the value of y for x = 14.5?

Predict the value of y for x = 9.0 ?

7.  For your study on the food consumption habits of teenage males you randomly select 10 teenage males and aske each how many 12 ounch servings soda he drinks each day. The results are below. At a=0.01, is there enough evidence to support the claim that teenage males drink fewer than three 12ounce servings of soda per day? Assume the population is normally distributed?

3.4

2.9

2.6

2.1

1.9

3.9

2.6

3.6

3.5

1.2

Write the claim mathematically and identify Ho and Ha ?

Use technology to find the P-value

Decide whether to reject or fail to reject the null hypothesis?

Interpret the decision in the context of the original claim.

8. An employment information service claims the mean annual pay for the full-time male workers over age 25 without a high school diploma is $22,350. The annual pay for a random sample of 10 full-time workers over age 25 without a high school diploma is listed. At a=0.10, test the claim that the mean salary is $22,350. Assume the population is normally distributed.

20,650

21,135

22,355

21,399

22,974

16,914

19,150

23,194

24,187

26,287

 

Write the claim mathematically and identify Ho and Ha ?

Find the critical value and identify the rejection region?

Find the standardized test statistic.

Decide whether to reject or fail to reject the null hypothesis?

Interpret the decision in the context of the original claim.?

9. A company that makes cola drinks states that the mean caffeine content per 12-ounch bottle of cola is 50milligrams. You want to test this claim. During your test you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 49.3 milligrams with a standard deviation of 6.6 milligrams. At a=0.02, can you reject the companys claim?

 

Write the claim mathematically and identify Ho and Ha ?

Find the critical value and identify the rejection region?

Decide whether to reject or fail to reject the null hypothesis?

10. The altitude (in thousands of feet) and speed of a plane(in feet per second) for various altitudes is shown below.

Altitude, x

Speed, y

0

962.2

5

1106.8

10

981.8

15

1016.8

20

994.7

25

1007.8

30

1033.1

35

1104.9

The correlation is strong or weak  AND positive or  negative linear correlation?

 

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