1. A study was carried out to investigate whether there is a relationship betwee

Question

1. A study was carried out to investigate whether there is a relationship between the percent of hearing loss and the volume at which people typically listen to music. Ten high school students agreed to participate in a study. Each was given a music player with headphones and was asked to listen to music for 10 minutes. The students were told to adjust the volume to a comfortable setting. After 10 minutes, the volume setting, which ranges from 1 to 10, was observed for each student. Each student then took a hearing test, and a measure of hearing loss (in percent) was recorded. The data are shown in the table below.

Use technology to calculate the correlation coefficient, and explain what you can infer about this relationship from the correlation coefficient. Specifically interpret the strength and direction of trend for this data.

2. The heights (in centimeters) and arm spans spans (in centimeters) of 31 students were measured. The association between x (height) and y (arm span) is shown in the scatterplot below. The equation of the least-squares regression line for this association is also given.  

estimated armspan = 4.5 + 0.977(height)

a. Jane is 158 cm tall and has an arm span of 154 cm. Rhonda is 163 cm tall and has an arm span of 165 cm. Does the line of best fit equation give a more accurate predicted value for Jane or Rhonda? Explain.

b. Doug is 210 cm tall. Would you use this least-squares regression line to predict his arm span? Explain.

3. What is the probability that a randomly selected person will be Male OR have Pneumonia? Write your answer as a decimal rounded to 3 places. EXPLAIN how you calculated this result.

4. GIVEN that a randomly selected person is a male, what is the probability he has Pneumonia? Write your answer as a decimal rounded to 3 places.

5. A couple decides that they will have 2 children. Assume that the probability of having a boy or a girl is equally likely. (Also assume that there are no twins. The couple has one child each time, and the events are independent)

Part 1: List all possible outcomes in the sample space. For example, one would be BB (having two boys). Give the other 3 possibilities.

Part 2: What is the probability that they will have only one girl?

Explanation / Answer

By using calculator we got the

correlation coefficient r = 0.89

There exists a positive correlation between volume settings and hearing loss.

Also they form a strong relationship between volume settings and hearing loss also there exists a linear trend.

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