# Project #24706 - statistics

Be sure to show all your work.

1.       Identify the population, and the sample in each of the following:

a.       A study of 33,043 infants in Italy was conducted to find a link between a heart rhythm abnormality and

sudden infant death syndrome.

b.       A survey of 1023 American households found that 65% of the households subscribe to cable television.

c.        A survey of 546 American women found that 56% of them are are the primary investor in their household.

d.       A survey of 872 American vacationers found that they planned on spending at least \$1800 dollars for their next vacation.

2.       A supermarket chain wants to verify that the bottler of their store brand of soda is in fact filling the cans to the

specified volume.  They took several “cubes” from the shelves and measured the amount in each can.  Is this an observational study or a designed experiment. Explain your answer.

3.       The manufacturer of Sleepeze has asked you to test the effectiveness of the drug. You decide to test the

effectiveness using the drug and a placebo. You select a select a group of 500 subjects and randomly assign them to either the treatment group or the placebo group.

a.       Is this an observational study or a designed experiment?

b.       If this is an experiment, diagram the experiment.

c.        You decide to “double blind” the study. What does that mean?

4.   A corporation that owns several large tree farms must determine the volume of each tree to decide if it should be

harvested. In order for the volume of a tree to be measured, the tree must be cut down. This is a very expensive

method of measuring volume, since money is lost if a tree is cut down before its volume is large enough to make

the maximum profit. The corporation would like to find a method of measuring tree volume that does not require

cutting  down trees. If there is a relationship between the volume of a tree and its circumference, then

circumference could be used to predict volume. Measuring circumference does not require cutting down trees.

To study the relationship, a simple random sample of 36 trees was selected from a large tree farm and cut down.

a.       Looking at the scatterplot of the data, what does it tell you about the relationship between the circumference and the volume?

b.     Find the equation of the least squares line of regression.

c.        What does the correlation coefficient tell you about the relationship between the circumference and the volume?

d.       If a tree has a circumference of 95 inches, predict the volume of this tree.

e.        Are you confident that predictions based on the equation of the least squares line of regression will be quite accurate?  Why or why not?

f.        What percent of the variation in the volume can be explained by the regression on the circumference?

Simple Linear Regression

Simple linear regression results:

Dependent Variable: Volume

Independent Variable: Circumference

Volume = (-69.389) + 2.81686 * Circumference

Sample Size = 36

R (Correlation Coefficient) = 0.974

R-sq. = 94.9%

 Subject Mathematics Due By (Pacific Time) 03/09/2014 09:00 pm
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