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Given a product X = ITi ∈I Xi of topological spaces (Xi , T ), with product topology, and a directed set J , a net in X indexed by J is given by a doubly indexed family {x ji } j ∈ J,i ∈I . Show that such a net converges for the product topology if and only if for every i ∈ I , the net {x ji } j ∈ J converges in Xi for Ti . (For this reason, the product topology is sometimes called the topology of "pointwise convergence": for each j , we have a function i f→ xij on I , and convergence for the product topology is equivalent to convergence at each "point" i ∈ I . This situation comes up especially when the Xi are [copies of] the same space, such as R with its usual topology. Then ITi Xi is the set of all functions from I into R, often called RI .)
Is there sufficient evidence at the 0.05 level of significance to conclude that the proportion of women physicians at the university health system exceeds 27.9%?
calculate the Pearson product-moment correlation coefficient and test for significance at the .01 level and calculate a t-test and test for significance at the .05 level, 2-tailed level of significance.
If an overrun contract was bid at 12 million dollars, what does the least-squares line predict for the cost of overrun (as a percent of bid price)?
At the 5% level of significance, test whether the proportion of internet users paying bills online is now more than 50%.
a group of statistics students decided to conduct a survey at their university to find the average mean amount of time
the probability of a student getting a a grade in an economics class is .24 and that of getting a b grade is .28. what
some types of periodicals are often browsed on the shelves but seldom purchased. a popular home improvement magazine
If probability of getting sample mean x less than unreported sample mean is 0.025, determine value of the unreported sample mean?
a researcher would like to know whether there is a consistent predictable relationship between verbal skills and math
A manufacturer of flashlight batteries took a sample of 13 batteries from a day's production and used them continuously until they failed to work.
Determine the sample size needed in order to be 99% confident that the sample proportion of the current customer accounts is within .03 of the true proportion of all current accounts for this company.
State the null and alternative hypotheses using proper Statistical Notation
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