Consider a thin spherical shell located between r = 0.49a0 and 0.51a0. for the n = 2, l = 1 state of hydrogen, find the probability for the electron to be found in a small volume element that subtends a polar angle of 0.11° and an azimuthal angle of 0.25° if the center of the volume element is located at: θ=5°, ϕ=60°. probability when n=2, l=1, m=0probability when n=2, l=1, m=±1

Arecent study focused on the number of times men and women who live alone buy take-out dinner in a month. assume that the distributions follow the normal probability distribution and the population standard deviations are equal. the information is summarized below. statistic men women sample mean 24.85 21.33 sample standard deviation 5.54 4.93 sample size 34 36 at the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? state the decision rule for 0.01 significance level: h0: μmen= μwomen h1: μmen ≠ μwomen. (negative amounts should be indicated by a minus sign. round your answers to 3 decimal places.) compute the value of the test statistic. (round your answer to 3 decimal places.) what is your decision regarding the null hypothesis? what is the p-value? (round your answer to 3 decimal places.)