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For the pull-off force data, the sample range is r 13.6 12.3 1.3. Generally, as the variability in sample data increases, the sample range increases. The sample range is easy to calculate, but it ignores all of the information in the sample data between the largest and smallest values. For example, the two samples 1, 3, 5, 8, and 9 and 1, 5, 5, 5, and 9, both have the same range (r 8). However, the standard deviation of the rst sample is s1 3.35, while the standard deviation of the second sample is s2 2.83. The variability is actually less in the second sample. Sometimes, when the sample size is small, say n 8 or 10, the information loss associated with the range is not too serious. For example, the range is used widely in statistical quality control where sample sizes of 4 or 5 are fairly common. We will discuss some of these applications in 16. EXERCISES FOR SECTIONS 6-1 AND 6-2

17

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6-1. Eight measurements were made on the inside diameter of forged piston rings used in an automobile engine. The data (in millimeters) are 74.001, 74.003, 74.015, 74.000, 74.005, 74.002, 74.005, and 74.004. Calculate the sample mean and sample standard deviation, construct a dot diagram, and comment on the data. 6-2. In Applied Life Data Analysis (Wiley, 1982), Wayne Nelson presents the breakdown time of an insulating uid between electrodes at 34 kV. The times, in minutes, are as follows: 0.19, 0.78, 0.96, 1.31, 2.78, 3.16, 4.15, 4.67, 4.85, 6.50, 7.35, 8.01, 8.27, 12.06, 31.75, 32.52, 33.91, 36.71, and 72.89. Calculate the sample mean and sample standard deviation. 6-3. The January 1990 issue of Arizona Trend contains a supplement describing the 12 best golf courses in the state. The yardages (lengths) of these courses are as follows: 6981, 7099, 6930, 6992, 7518, 7100, 6935, 7518, 7013, 6800, 7041, and 6890. Calculate the sample mean and sample standard deviation. Construct a dot diagram of the data. 6-4. An article in the Journal of Structural Engineering (Vol. 115, 1989) describes an experiment to test the yield strength of circular tubes with caps welded to the ends. The rst yields (in kN) are 96, 96, 102, 102, 102, 104, 104, 108, 126, 126, 128, 128, 140, 156, 160, 160, 164, and 170. Calculate the sample mean and sample standard deviation. Construct a dot diagram of the data. 6-5. An article in Human Factors (June 1989) presented data on visual accommodation (a function of eye movement) when recognizing a speckle pattern on a high-resolution CRT screen. The data are as follows: 36.45, 67.90, 38.77, 42.18, 26.72, 50.77, 39.30, and 49.71. Calculate the sample mean and sample standard deviation. Construct a dot diagram of the data.

EXERCISES FOR SECTION 12-2

To create a custom layout, click the View tab on the Ribbon and click the Slide Master button. In the Slide Master pane, click the Insert Layout button on the Slide Master tab. Click the bottom half of the Insert Placeholder button, click a slide object type and click and drag to set the object s size and placement.

Although an extra layer of code sits on top of the COM component, this generally operates faster than its late bound counterpart.

12-13 Consider the regression model fit to the soil shear strength data in Exercise 12-1 (a) Test for significance of regression using 005 What is the P-value for this test (b) Construct the t-test on each regression coefficient What are your conclusions, using 005 12-14 Consider the absorption index data in Exercise 12-2 The total sum of squares for y is SST 74200 (a) Test for significance of regression using 001 What is the P-value for this test (b) Test the hypothesis H0: 1 0 versus H1: 1 0 using 001 What is the P-value for this test What conclusion can you draw about the usefulness of x1 as a regressor in this model 12-15 Consider the NFL data in Exercise 12-4 (a) Test for significance of regression using 005.

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