37. Eat your kale: Kale is a type of cabbage commonly found in salad and used in cooking in many parts of the world. Six measurements were made of the mineral content (in percent) of kale, with the following results. 26.1 17.5 15.4 16.4 15.1 12.8 It turns out that the value 26.1 came from a specimen that the investigator forgot to wash before measuring. a. The data contain an outlier that is clearly a mistake. Eliminate the outlier, then construct a 95% confidence interval for the mean mineral content from the remaining values. b. Leave the outlier in and construct the 95% confidence interval. Are the results noticeably different? Explain why it is important to check data for outliers. Source: Journal of Nutrition 66:55-66

- TABLE 6E.2 Bearing Diameter Data Sample Number i Sample Number R 1 34.5 3 13 35.4 8. 2 34.2 4 14 34.0 6 3 31.6 4 15 37.1 5 4 31.5 4 16 34.9 7 5 35.0 5 17 33.5 4 34.1 6. 18 31.7 3 7 32.6 4 19 34.0 8. 8 33.8 3 20 35.1 4. 9. 34.8 7 21 33.7 2 10 33.6 8 22 32.8 1 11 31.9 3 23 33.5 3 12 38.6 9 24 34.2 2 inside diameter of the bearing, with only the last three decimals recorded (i.e., 34.5 should be 0.50345). (a) Set up ī and R charts on this process. Does the process seem to be in statistical control? If nec- essary, revise the trial control limits. (b) If specifications on this diameter are 0.5030 ± 0.0010, find the percentage of nonconforming bearings produced by this process. Assume that diameter is normally distributed.

You have been hired to measure the concentration of ammonia in water from wells at two districts on Long Island. After sampling 10 wells in one of the districts you find the values are, in mg/L: 6.4, 2.1, 1.4, 0.7, 6.8, 3.2, 2.7, 1.6, 4.9, 1.2. Your assistant plots the data from the second set of wells and the histogram of data from that sample looks pretty much the same as for your data set. Which statistical test do you anticipate that you will use? An one-sample t-test An unpaired, two-sample t-test A paired, two-sample t-test A one-way anova A Mann-Whitney U test Main Content

No tortilla chip aficionado likes soggy chips, so it is important to find characteristics of the production process that produce chips with an appealing texture. The following data on x = frying time (sec) and y = moisture content (%) appeared in an article. x 5 10 15 20 25 30 45 60 y 16.4 9.7 8.1 4.2 3.3 2.8 2.0 1.2 (a) Construct a scatter plot of y versus x. y 15 10- 5 y 15 O 10 10 20 30 40 50 5 10 20 10 NE X 50 60 30 60 40 X 15 y 10 O 5 O y 15 10 20 30 40 50 60 10 20 30 Comment. The plot has a curved pattern. A linear model would not be appropriate. O The plot has a curved pattern. A linear model would be appropriate. O The plot does not have a curved pattern. A linear model would be appropriate. O The plot does not have a curved pattern. A linear model would not be appropriate. 40 50 60 X X

1.8 A Canadian manufacturer identified a critical diameter on a crank bore that needed to be maintained within a close tolerance for the product to be successful. Sam- ples of size 4 were taken every hour. The values of the differences (measurement - specification), in ten- thousandths of an inch, are given in Table 1.4. (a) Calculate the central line for an X-bar chart for the 24 hourly sample means. The centerline is x = — . . . (4.25 -3.00 -1.50 +3.25)/24. = (b) Is the average of all the numbers in the table, 4 for each hour, the same as the average of the 24 hourly averages? Should it be? (c) A computer calculation gives the control limits LCL = -4.48 UCL 7.88 = Construct the X-bar chart. Identify hours where the process was out of control.

Systolic coefficients of variation are 14.2% and the Diastolic is 17%   The coefficients of variation for each data set are:   a. more than 5 percentage points apart   b. within 5 percentage points of each other     ​Therefore, the systolic measurements vary   a. about the same as   b. significantly more than    c. significantly less than the diastolic measurements.

Periodically, the county Water Department tests the drinking water of homeowners for contaminants such as lead and copper. The lead and copper levels in water specimens collected in 1998 for a sample of 10 residents of a subdevelopement of the county are shown below. lead (g/L) 2.9 0.2 5.1 4.2 5.5 1.2 0.133 0.774 0.214 0.671 0.444 0.234 0.357 0.761 0.176 0.888 (a) Construct a 99% confidence interval for the mean lead level in water specimans of the subdevelopment. OSMOSO copper (mg/L) 0.3 1.3 4.9 1.7 (b) Construct a 99% confidence interval for the mean copper level in water specimans of the subdevelopment. OSHSO

b?

A?

could you write with a pen and paper?