Make the following tests of hypotheses. State the conclusion in each case. 79, H₁: µ ‡ 79, n = 32, x = 76.4, o = 13, α = 0.1. a. Ho: μ = We b. Ho: M = We ✓ Ho. We 30, H₁: μ< 30, n = 74, x = 25.4, o = 7.1, α = 0.05. ✓ Ho. c. Ho: M = 51, H₁: µ > 51, n = 36, x = 57.5, o = 3.6, α = 0.03. Ho.

56. Let P(A) = 0.2, P(B) = 0.5, and P[(A n B)'] = 0.88. Find.. a. P(ΑnB) b. P(AUB) С. P(B|A)

The length of a component is to be estimated through repeated measurement. Ten independent measurements are made with an instrument whose uncertainty is 0.05 a. mm. Let denote the average of these measurements. Find the uncertainty in 7. b. A new measuring device, whose uncertainty is only 0.02 mm, becomes available. Five independent measurements are made with this device. Let y denote the average of these measurements. Find the uncertainty in y. In order to decrease the uncertainty still further, it is decided to combine the estimates X and y. One engineer suggests estimating the length with (1/2)X + (1/2)Y. A second engineer argues that since X is base don 10 measurements, while y is based on only five, a better estimate is (10/15)X+ (5/15)F. Find the uncertainty in each of these C. estimates. Which is smaller? Find the value c such that the weighted average c + (1- c)Y has minimum uncertainty. Find the uncertainty in this weighted average. d.

Please give solution in correct and step by step detailed format thanku Don't give solution in image format

_11. Which expression does NOT equal 25n12? а. (5nб)2 b. (5n°)(5n9) c. 25(n3)8 d. 5(n2)8

Find C(n, x)p*q" - × for the given values of n, x, and p. (Round your answer to four decimal places.) 1 n = 5, x = 3, p 4

(Use table provided and an excel sheet to show formulas used to answer the questions)

Find C(n, x)p*q" - *for the given values of n, x, and p. (Round your answer to four decimal places.) n = 8, x = 5, p =

Why is it (2n-1)*pi/2. Can you please explain it to me. Thank you

Consider the hypotheses below. H0​: μ=50 H1​: μ≠50 Given that x=57​, s=12​, n=30​, and α=0.05​, answer the questions below.