1. Intro to Stats and Collecting Data

Control Limits In a control chart, what are upper and lower control limits, and what is their purpose?

Time and Motion In a physics experiment at Doane College, a soccer ball was thrown upward from the bed of a moving truck. The table below lists the time (sec) that has lapsed from the throw and the corresponding height (m) of the soccer ball.

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a. Find the value of the linear correlation coefficient r.

Time and Motion In a physics experiment at Doane College, a soccer ball was thrown upward from the bed of a moving truck. The table below lists the time (sec) that has lapsed from the throw and the corresponding height (m) of the soccer ball.

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b. Based on the result from part (a), what do you conclude about a linear correlation between time and height?

Sum of Squares Criterion In addition to the value of another measurement used to assess the quality of a model is the sum of squares of the residuals. Recall from Section 10-2 that a residual is (the difference between an observed y value and the value predicted from the model). Better models have smaller sums of squares. Refer to the U.S. population data in Table 10-7.

a. Find the sum of squares of the residuals resulting from the linear model.

Exercises 1–10 are based on the following sample data consisting of costs of dinner (dollars) and the amounts of tips (dollars) left by diners. The data were collected by students of the author.

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Scatterplot Construct a scatterplot and comment on the pattern of points.

Pepsi Cans. In Exercises 5–8, refer to the axial loads (pounds) of aluminum Pepsi cans that are 0.0109 in. thick, as listed in Data Set 41 “Aluminum Cans” in Appendix B. An axial load of a can is the maximum weight supported by the side, and it is important to have an axial load high enough so that the can isn’t crushed when the top lid is pressed onto the top. There are seven measurements from each of 25 days of production. If the 175 axial loads are in one column, the first 7 are from the first day, the next 7 are from the second day, and so on, so that the “subgroup size” is 7.

Pepsi Cans: Run Chart Treat the 175 axial loads as a string of consecutive measurements and construct a run chart. What does the result suggest?

Quarters. In Exercises 9–12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available in Data Set 44 “Weights of Minted Quarters” in Appendix B.

Quarters: Notation Find the values of x(doublebar) and Rbar. Also find the values of LCL and UCL for an R chart.

Quarters. In Exercises 9–12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available in Data Set 44 “Weights of Minted Quarters” in Appendix B.

Quarters: R Chart Treat the five measurements from each day as a sample and construct an R chart. What does the result suggest?

Quarters. In Exercises 9–12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available in Data Set 44 “Weights of Minted Quarters” in Appendix B.

Quarters: xbar Chart Treat the 5 measurements from each day as a sample and construct an xbar chart. What does the result suggest?

Identify three specific criteria for determining when a process is out of statistical control.

Notation The control chart for Exercise 1 shows a value of p_bar = 0.0975. What does that value denote, and how is it obtained? What do UCL and LCL indicate?

Control Limits In constructing a control chart for the proportions of defective dimes, it is found that the lower control limit is -0.00325. How should that value be adjusted?

Minting Quarters Specifications for a quarter require that it be 8.33% nickel and 91.67% copper; it must weigh 5.670 g and have a diameter of 24.26 mm and a thickness of 1.75 mm; and it must have 119 reeds on the edge. A quarter is considered to be defective if it deviates substantially from those specifications. A production process is monitored, defects are recorded and the accompanying control chart is obtained. Does this process appear to be within statistical control? If not, identify any out-of-control criteria that are satisfied. Is the manufacturing process deteriorating?

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Control Charts for p. In Exercises 5–12, use the given process data to construct a control chart for p. In each case, use the three out-of-control criteria listed near the beginning of this section and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply.

Euro Coins Consider a process of minting coins with a value of one euro. Listed below are the numbers of defective coins in successive batches of 10,000 coins randomly selected on consecutive days of production.

32 21 25 19 35 34 27 30 26 33

Quarters. In Exercises 9–12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available in Data Set 44 “Weights of Minted Quarters” in Appendix B.

Find the values of LCL and UCL for an xbar chart.