6.3 Problem Set

1) Malia turned the water on in her bathtub full blast. She then measured the depth of the water every two minutes until the bathtub was full. Her findings are listed in the following table. In section 6.1 we constructed a scatterplot and described the plot, we are now going to analyze this data further.

a) Construct a scatterplot on your graphing calculator (or computer). Sketch the graph that the calculator shows. Be sure to label your axes.

b) Calculate the Least-Squares Regression Line (LSRL) using your calculator. Report your equation. Be sure to identify your variables.

c) Calculate the correlation coefficient (r). Report it here. What are the two things that this number tells us about this graph?

d) Identify and interpret the slope in the context of the problem.

e) Using your equation, what is the predicted depth of the water after 17 minutes? After one hour?

f) Are your answers in (e) reasonable? Why or why not?

2) The following table shows the progression of the Federal Minimum Wage in the United States since 1938 (source:http://www.laborlawcenter.com). We are going to analyze the relationship between year and minimum wage to see if there is a predictable relationship between the variables.

a) Using year only as the explanatory variable (ignore month & day), construct a scatterplot. Sketch the graph that the calculator shows. Be sure to label your axes.

b) Describe the relationship between the two variables. (S.C.O.F.D.)

c) Calculate the Least-Squares Regression Line (LSRL). Add the line to your graph and report your equation. Be sure to identify your variables.

d) Calculate the correlation (r). Even though r is very high, do you feel that a line is the best model for this data? Why or why not?

e) Based on your model, what would you predict the Federal Minimum Wage to be in 2012? Is this an accurate prediction? Why or why not?

f) Based on your model, what would you predict the minimum wage to have been in 1968? How close is this to the actual minimum wage that year?

3) Suppose that some researchers analyzed the relationship between fathers' and sons' IQ scores for a group of men. Suppose further that they discovered that the relationship was reasonably linear and they calculated a regression line of

$\hat{y}= 12 + 0.9x$

where x = father's IQ and y = son's IQ.

a) Identify the explanatory and response variables.

b) Identify and interpret the slope in the context of the problem.

c) Identify and interpret the y-intercept in the context of the problem.

d) Do your answers to (b) and (c) seem reasonable? Why or why not?

e) What would you predict a son's IQ to be if his father has an IQ of 120? What if the father had an IQ of 140?

f) If you knew that the original data included fathers with IQs from 108 to 145, explain why it would be inappropriate to use your model to predict a son's IQ if his father's IQ were 170.

Review Exercises

(for 4 - 7) Suppose that Marco, the star of the basketball team, makes 79% of the free-throws that he attempts. Assuming that each free-throw is independent, answer the following questions.

4) What is the probability that Marco will make three free-throws in a row?

5) What is the probability that Marco will make exactly two out of three free-throws?

6) What is the probability that Marco will miss at least one of his next four free-throws?

7) If you were going to set up a simulation to estimate this scenario, which of the following would not be an appropriate way to assign the digits?

A. 01-79 represents makes, 80-99 & 00 represents misses

B. 01-21 represents misses, 22-99 & 00 represents makes

C. 00-79 represents makes, 80-99 represents misses

D. 00-20 represents misses, 21-99 represents makes

E. 00-78 represents makes, 79-99 represents misses

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