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Making Friends Online A survey conducted in March 2015 asked 1060 teens to estimate, on average, the number of friends they had made online. While \(43 \%\) had not made any friends online, a small number of the teens had made many friends online. (a) Do you expect the distribution of number of friends made online to be symmetric, skewed to the right, or skewed to the left? (b) Two measures of center for this distribution are 1 friend and 5.3 friends. \({ }^{31}\) Which is most likely to be the mean and which is most likely to be the median? Explain your reasoning.

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.)

Price Differentiating E-commerce websites "alter results depending on whether consumers use smartphones or particular web browsers," 34 reports a new study. The researchers created clean accounts without cookies or browser history and then searched for specific items at different websites using different devices and browsers. On one travel site, for example, prices given for hotels were cheaper when using Safari on an iPhone than when using Chrome on an Android. At Home Depot, the average price of 20 items when searching from a smartphone was \(\$ 230,\) while the average price when searching from a desktop was \(\$ 120 .\) For the Home Depot data: (a) Give notation for the two mean prices given, using subscripts to distinguish them. (b) Find the difference in means, and give notation for the result.

Does It Pay to Get a College Degree? In Exercise 2.21 on page \(58,\) we saw that those with a college degree were much more likely to be employed. The same article also gives statistics on earnings in the US in 2009 by education level. The median weekly earnings for high school graduates with no college degree was \(\$ 626,\) while the median weekly earnings for college graduates with a bachelor's degree was \(\$ 1025 .\) Give correct notation for and find the difference in medians, using the notation for a median, subscripts to identify the two groups, and a minus sign.

Create a Dataset Give any set of five numbers satisfying the condition that: (a) The mean of the numbers is substantially less than the median. (b) The mean of the numbers is substantially more than the median. (c) The mean and the median are equal.

For the datasets. Use technology to find the following values: (a) The mean and the standard deviation. (b) The five number summary. 10,11,13,14,14,17,18,20,21,25,28

For the datasets. Use technology to find the following values: (a) The mean and the standard deviation. (b) The five number summary. 25, 72, 77, 31, 80, 80, 64, 39, 75, 58, 43, 67, 54, 71, 60

Indicate whether the five number summary corresponds most likely to a distribution that is skewed to the left, skewed to the right, or symmetric. (15,25,30,35,45)

Indicate whether the five number summary corresponds most likely to a distribution that is skewed to the left, skewed to the right, or symmetric. (100,110,115,160,220)

Indicate whether the five number summary corresponds most likely to a distribution that is skewed to the left, skewed to the right, or symmetric. (22.4,30.1,36.3,42.5,50.7)