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1. Show that in any finite dimensional Banach space (Rk with any norm), for any closed, convex set C and any point x not in C , there is at least one nearest point y in C ; in other words, ly - x l= infz∈C lz - x l.
2. Give an example of a closed, convex set C in a Banach space S and an x ∈ S which has no nearest point in C . Hint: Let S be the space £1 of absolutely summable sequences with norm l{xn }l1 := },n |xn |. Let C := {{t j (1 + j )/j } j ≥1: t j ≥ 0, }, j t j = 1} and x = 0.
H: μ = 50. A sample of 25 scores is selected and the mean is M = 55.Assuming that the sample variance is s2 = 100, compute the estimated standard error and the t statistic.
We are asked to investigate the hypothesis that the number of crimes is related to police expenditures because states with higher crime rates are likely to increase their police force, thereby spending more on the number of officers on the street.
Assume the chief does not want his officers to cite a car for speeding unless they are 99% sure that it is travelling at 58 miles per hour or faster. What is the minimum estimate of speed at which a car should be cited for speeding?
quantitative research questiondownload gpower and play around with it. see how changes in assumptions and parameters
They found that those with higher levels of cigarette use had lower GPAs, and vice versa. What can you rightfully conclude from this? Why? Be specific about what this kind of information may indicate and mean.
a) 95% of confidence intervals generated will include the sample mean X. b) 5% of the confidence intervals generated will include the true mean μ
three fair regular eight-sided dice are rolled.a what is the probability that the sum of the die rolls is10?b what is
A nursing school wants to estimate the true mean annual income of its alumni. It randomly samples 120 of its alumni. The mean annual income was $58,700 with a standard deviation of $1,500.
their average cost was 340.00 with standard deviation of 80.00. Dean of students thinks that costs are greater this semester. Determine the test value for this hypothesis.
A researcher randomly assigns 12 participants to one of three weight-loss conditions (A-diet, B-exercise, C-medication). The researcher obtains the following data: What is the values of SStotal
describe the types of probability.classify the statement as an example of classical probability empirical probability
You are given cholesterol levels of 13 men and 12 women as below. Use Wilcoxan Rank-Sum Test. Sort 25 numbers and rank them from smallest to largest, and fill up the ranks in the table. b. Find µR and σR. Calculate test statistic z.
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