Assume that you have a sample of n 1 equals 4, with the sample mean Upper X overbar 1 equals 43, and a sample standard deviation of Upper S 1 equals 7, and you have an independent sample of n 2 equals 8 from another population with a sample mean of Upper X overbar 2 equals 32 and the sample standard deviation Upper S 2 equals 8. Assuming the population variances are equal, at the 0.01 level of significance, is there evidence that mu 1 greater than mu 2?

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?