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Part 1: Using the Library, web resources, and/or other materials, find the logarithmic formula that gives the pH of a substance. State what each variable in your equation represents.
Find the hydrogen ion content of a substance of your choice. Using this hydrogen ion content, show how to find the pH of the substance using the formula. Is this substance acidic or basic? Why? Round the pH to three decimal places.
Part 2: Suppose that the number of cars, C, on 1st Avenue in a city over a period of time t, in months, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of cars driven on 1st Avenue can be modeled by an exponential function, C= p * at where p is the number of cars on the road on the first day recorded. If you commuted to work each day along 1st Avenue, would you prefer that the value of a between 0 and 1 or larger than 1? Explain your reasoning.
Typing hint: Type formula above as C = p * a^t
Use these statistics to construct a 94% confidence interval for the mean monthly consumption for the population of all Ontario households.
Determine the probability that a sample proportion for n=30 is within 0.10 of the true population proportion of 0.40, which represents the proportion of cola drinkers who prefer a Coca-Cola drink.
Test whether there is a difference in the mean of times men and women and determine the p-value.
Test the hypothesis that there is no difference between the means of retailers (α= .05). Select a multiple comparison test, if necessary, to determine which groups differ in mean sales (α= .05).
Before starting the trial, a pilot study is conducted involving 7 participants. Is there a statistically significant difference in blood pressures overtime? Run the test at a 5% level of significance.
Two bonus points for rigorously proving Xt and Xt+1 are not independent. Let Xt=1+et-0.5et-1, t=1,2,3,..., where et~IID N(0,2), variance of et is 2. Calculate the mean of Xt.
A portfolio manager believes that tomorrow's foreign exchange rate of German marks per US dollar will be Normally distributed with mean 2.03 and standard deviation 0.08. Using the manager's numbers:
At the .05 significance level, can we conclude that the guideline is still reasonable?
As part of its testing program, LongLast tests a sample of 25 batteries. What is the standard error of the mean?
The cheetahs' coach believes that the Rockets' times are normally distributed as well. Construct a 95% confidence interval the Coach to compare the two teams' sprint units.
The company believes that it averages about the same weight per bag in each of two production lines. To test this idea, they will perform a hypothesis test to compare the two lines at the alpha level of 0.05. State the null and alternative hypothe..
Suppose a firm evaluates the productivity of the three shifts of workers who work in their factory. Each shift's performance is measured based on the amount of output that is produced during the shift - day, evening, or swing shift.
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