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1. Show, assuming AC, that any Cartesian product of finite sets is either finite or uncountable (can't be countably infinite).
2. Let X be the collection of all intervals [a, b] of length 0 ≤ b - a ≤ 2, with inclusion as partial ordering. Show that every chain in X has an upper bound.
3. In the application of the recursion principle 1.3.2 in the proof that WO implies HMP, how should g be defined? Show that the resulting argument does prove that WO implies HMP.
Let x1,..., x16 be an independent sample from a normal distribution N(μ, 5). For the following test problem: Ho: μ = 6.5 ↔Ha: μ ≠6.5, let the rejection region be W = {|x-6.5| ≥ c}, If μ = 7.5 is correct, find the probability of the second type erro..
a sketch a t -v diagram then draw a circle to indicate the region where you are guaranteed to find ideal gas states on
High temp for January 1st is normally distributed with a mean of 40 degrees and a standard deviation of 5 degrees.
a brewerys filling machine is adjusted to fill bottles with a mean of 31.1 oz. of ale and a variance of 0.007.
Roger has read a report that the weights of adult mail Siberian tigers have a distribution which is approximately normal with mean μ = 390 lb and σ = 65 lb
Suppose the distribution of amounts purchased follows normal distribution. For sample of 50 customers, reply the following questions. Determine the probability the sample mean is at least $25.00?
A market research company surveyed consumers to determine their ranked preferences of energy drinks among the brands Monster, Red Bull, and Rockstar.
a. What is the probability of a type I error? b. Give the formula for the test statistic.
a study conducted at a certain college shows that 55 of the schools graduates find a job in their chosen field within a
question a researcher hypothesizes that individuals who listen to classical music will score differently from the
What decision should be made regarding the null hypothesis?
Customers who enter the store, and ask them if they have a Ralph's card. Suppose they solicit 400 customers one day, and find that 160 of them have a Ralph's card.
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