Which of the following are subspaces of p3? support your answer.
a. u = { f(x) | f(x) ∈ p3, f(2) = 1}
b. u = {xg(x) | g(x) ∈ p2}
c. u = {xg(x) | g(x) ∈ p3}
d. u = {xg(x) + (1−x)h(x) | g(x) and h(x) ∈ p2}
e. u = the set of all polynomials in p3 with constant term 0
f. u = { f(x) | f(x) ∈ p3, deg f(x) = 3}

A. find the power of the test, when the null hypothesis assumes a population mean of mu = 450, with a population standard deviation of 156, the sample size is 5 and the true mean is 638.47 with confidence intervals of 95 b. find the power of the test, when the null hypothesis assumes a population mean of mu = 644, with a population standard deviation of 174, the sample size is 3 and the true mean is 744.04 with confidence intervals of 95% c. find the power of the test, when the null hypothesis assumes a population mean of mu = 510, with a population standard deviation of 126, the sample size is 10 and the true mean is 529.44 with confidence intervals of 95