g where C>0 is a constant known as the threshold that you will choose in designing the test. (In the previous problem, C was chosen to be 0.25.) On observing the data set, if ψ=1, you will reject H0. If ψ=0, then you will fail to reject H0. Suppose that indeed μ=0. Then P(ψC=1), the probability of rejecting H0, quantifies how likely we are to make the error of rejecting H0 even though H0 holds. Under the assumption that H0:μ=0, for which value of C is P(ψC=1) likely the largest? C=0.01 C=0.1 C=0.5 C=1.0

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?