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# Significance of Correlation & Confidence Interval

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a. The use of electrical stimulation (ES) to increase muscular strength is discussed in the Journal of Orthopedic and Sports Physical Therapy. Seventeen healthy volunteers participated in the experiment. Muscular strength, Y, was measured as a torquein foot-pounds, and ES, X, was measured in mA (microamps). The equation for the line of best fit is given as Y = 1.8X + 28.7, and the Pearson correlation coefficient was 0.61.a. Was the correlation coefficient significantly different from zero? Use &#945; = 0.05.b. Predict the torque for a current equal to 50 mA.

b.
In the autumn of 2003, the National Safe Kids Campaign conducted a study of helmet use among children ages 5 to 14 who participate in wheeled sports. Data were collected from various sites across the United States that were designated as places where children often engage in wheeled sports. Activity, apparent gender, and estimated age were recorded for each rider, along with information on helmet use. It was found that, overall, 41% of children were wearing a helmet while participating in a wheeled sport.
b. Identify the parameter of interest.
c. Identify the statistic and give its value.
d. Classify the four variables as numerical or attribute.

c.
A coin is flipped three times.
a. Draw a tree diagram that represents all possible outcomes.
b. Identify all branches that represent the event "exactly one head occurred."
c. Find the probability of "exactly one head occurred."

d.
A chemist is testing a newly proposed analytical method and decides to use the currently accepted method for comparison. She takes 12 specimens of unknown concentrate and determines the concentration of each specimen, using both the proposed method and the current method. Do these two samples represent dependent or independent samples? Explain.

e.
The weights of full boxes of a certain kind of cereal are normally distributed with a standard deviation of 0.27oz. A sample of 18 randomly selected boxes produced a mean weight of 9.87 oz.
a. Find the 95% confidence interval for the true mean weight of a box of this cereal.
b. Find the 99% confidence interval for the true mean weight of a box of this cereal.
c. What effect did the increase in the level of confidence have on the width of the confidence interval?