Chapter 2: Problem 49
Draw any dotplot to show a dataset that is Clearly skewed to the left.
Chapter 2: Problem 49
Draw any dotplot to show a dataset that is Clearly skewed to the left.
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Get started for freeFor the datasets. Use technology to find the following values: (a) The mean and the standard deviation. (b) The five number summary. 4, 5, 8, 4, 11, 8, 18, 12, 5, 15, 22, 7, 14, 11, 12
Arsenic in Toenails Arsenic is toxic to humans, and people can be exposed to it through contaminated drinking water, food, dust, and soil. Scientists have devised an interesting new way to measure a person's level of arsenic poisoning: by examining toenail clippings. In a recent study, \(, 9\) scientists measured the level of arsenic (in \(\mathrm{mg} / \mathrm{kg}\) ) in toenail clippings of eight people who lived near a former arsenic mine in Great Britain. The following levels were recorded: \(\begin{array}{llllll}0.8 & 1.9 & 2.7 & 3.4 & 3.9 & 7.1\end{array}\) \(\begin{array}{ll}11.9 & 26.0\end{array}\) (a) Do you expect the mean or the median of these toenail arsenic levels to be larger? Why? (b) Calculate the mean and the median. 2.62 Fiber in the Diet The number of grams of fiber eaten in one day for a sample of ten people are \(\begin{array}{ll}10 & 11\end{array}\) \(11 \quad 14\) \(\begin{array}{llllll}15 & 17 & 21 & 24 & 28 & 115\end{array}\) (a) Find the mean and the median for these data. (b) The value of 115 appears to be an obvious outlier. Compute the mean and the median for the nine numbers with the outlier excluded. (c) Comment on the effect of the outlier on the mean and on the median.
Two variables are defined, a regression equation is given, and one data point is given. (a) Find the predicted value for the data point and compute the residual. (b) Interpret the slope in context. (c) Interpret the intercept in context, and if the intercept makes no sense in this context, explain why. Study \(=\) number of hours spent studying for an exam, Grade \(=\) grade on the exam. \(\widehat{\text { Grade }}=41.0+3.8\) (Study); data point is a student who studied 10 hours and received an 81 on the exam.
Donating Blood to Grandma? Can young blood help old brains? Several studies \(^{32}\) in mice indicate that it might. In the studies, old mice (equivalent to about a 70 -year-old person) were randomly assigned to receive blood plasma either from a young mouse (equivalent to about a 25 -year-old person) or another old mouse. The mice receiving the young blood showed multiple signs of a reversal of brain aging. One of the studies \(^{33}\) measured exercise endurance using maximum treadmill runtime in a 90 -minute window. The number of minutes of runtime are given in Table 2.17 for the 17 mice receiving plasma from young mice and the 13 mice receiving plasma from old mice. The data are also available in YoungBlood. $$ \begin{aligned} &\text { Table 2.17 Number of minutes on a treadmill }\\\ &\begin{array}{|l|lllllll|} \hline \text { Young } & 27 & 28 & 31 & 35 & 39 & 40 & 45 \\ & 46 & 55 & 56 & 59 & 68 & 76 & 90 \\ & 90 & 90 & 90 & & & & \\ \hline \text { Old } & 19 & 21 & 22 & 25 & 28 & 29 & 29 \\ & 31 & 36 & 42 & 50 & 51 & 68 & \\ \hline \end{array} \end{aligned} $$ (a) Calculate \(\bar{x}_{Y},\) the mean number of minutes on the treadmill for those mice receiving young blood. (b) Calculate \(\bar{x}_{O},\) the mean number of minutes on the treadmill for those mice receiving old blood. (c) To measure the effect size of the young blood, we are interested in the difference in means \(\bar{x}_{Y}-\bar{x}_{O} .\) What is this difference? Interpret the result in terms of minutes on a treadmill. (d) Does this data come from an experiment or an observational study? (e) If the difference is found to be significant, can we conclude that young blood increases exercise endurance in old mice? (Researchers are just beginning to start similar studies on humans.)
Two variables are defined, a regression equation is given, and one data point is given. (a) Find the predicted value for the data point and compute the residual. (b) Interpret the slope in context. (c) Interpret the intercept in context, and if the intercept makes no sense in this context, explain why. Weight \(=\) maximum weight capable of bench pressing (pounds), Training = number of hours spent lifting weights a week. Weight \(=95+11.7\) (Training); data point is an individual who trains 5 hours a week and can bench 150 pounds.
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