Chapter 2: Problem 99
Find and interpret the z-score for the data value given. The value 88 in a dataset with mean 96 and standard deviation 10.
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Sketch a curve showing a distribution that is symmetric and bell-shaped and has approximately the given mean and standard deviation. In each case, draw the curve on a horizontal axis with scale 0 to 10. Mean 3 and standard deviation 1.
Find and interpret the z-score for the data value given. The value 8.1 in a dataset with mean 5 and standard deviation 2
The Wind Map The website hint.fm/wind/ shows the current wind patterns across the US. In order to generate this map, what two variables are being recorded at weather stations across the US?
Indicate whether the five number summary corresponds most likely to a distribution that is skewed to the left, skewed to the right, or symmetric. (0,15,22,24,27)
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.)
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