In a study of streams and hard water in the Adirondack Mountains, a researcher wanted to determine if there is a relationship between the water’s pH and its hardness (in grains). From a sample of 172 streams, does the data suggest that there is a positive correlation between pH and hardness of water?  The relevant sample statistic is 0.710 with a standard error of 0.077.  The resulting p-value is 0.000. Correctly complete the p-value interpretation below: The chance of seeing a sample [answer1] of [answer2] or any value [answer3] is 0.000, when assuming the population correlation is [answer4].

We have access to the complete dataset of all ages (in years) at death for First Ladies of the U.S. who have passed. From this data set we know that the average age at death is 71.7 years. You are interested in how the sample statistics vary for different samples of size n=15 from this population.   A sampling distribution is constructed where one of the samples is used to create a bootstrap distribution.    This sample has mean: x-bar = 78 years. Below are boxplots of the sample of size n = 15, the sampling distribution, and the bootstrap distribution (although not necessarily in that order!).  Use all of the provided information to select the correct reason for each Boxplot identification. Boxplot A is the sample of n = 15 because it is centered at the [answer5] where the sample standard deviation (s) is [answer6] the value of the standard error found with the sampling distribution. Boxplot B is the sampling distribution because it is centered at the [answer1] and has a standard error that is roughly equal to the estimated standard error found with the [answer2]. Boxplot C is the bootstrap distribution because it is centered at the [answer3] and has an estimated standard error that is roughly equal to the standard error found with the [answer4].

What would be the charge on an atom of lead which only has 78 electrons?  [sign][magnitude]

Consider an element that has 3 naturally occurring isotopes. The isotopic masses and percent abundances are 53.9396 amu (5.845%), 55.9349 amu (91.754%), and 56.9354 amu.  What is the average atomic mass in amu of X? Show your work and give your answer to 2 decimal places.

Carl Fredricksen raised 80 sheep, then entered into a series of business transactions. He traded all the sheep for goats at an exchange rate of 5 goats for 7 sheep. Next, he exchanged all the sheep for hogs at a rate of 4 goats for 2 hogs weighing 225 lbs. each. He sold all the hogs at a market price of $60.00 per 100.0 lbs. How much money did he make from the 60 goats?  Show your work using dimensional analysis.

For the reaction CaCO3(s) + 2 HCl(aq) →  CaCl2(aq) + CO2(g) + H2O(l) If 78.1 g solid CaCO3 is mixed with 51.6 g HCl. Which one will be the limiting reactant? Show your work and explain your reasoning.

A chemist is trying to identify an unknown metal and finds that 25.0 cm³ of the substance has a mass of 224.43 g at 20°C. Which of the following metals is it? Show your work.

Cucamongine (symbol Cg) is a fictional name for one of the halogens. Note that the name ends with -ine just as the halogen names used by ordinary chemists. According to the naming rules for the oxyanions of halogens, what would be the name of CgO2¯? Explain your reasoning.

What would be the charge on an atom of gold which only has 78 electrons?  [sign][magnitude]

The names and symbols for the transition elements used in the fictional kingdom of Narnia are different from those used by the rest of the planet, except for silver, cadmium, and zinc. For the rest of the elements and chemical entities, the kingdom uses the same names and inorganic nomenclature rules as used by the rest of the world. If the name used for a transition metal is “narnium” (symbol Nr), what would be the name of NrSO4 in the kingdom of Narnia? Explain your reasoning.