The following data lists the ages of a random selection of actresses when they won an award in the category of best actress, along with the ages of actors when they won in the category of best actor. the ages are matched according to the year that the awards were presented. complete parts (a) and (b) below. actress left parenthesis years right parenthesis 31 26 31 30 32 23 24 44 32 31 actor left parenthesis years right parenthesis 67 37 33 35 26 37 53 36 36 46 a. use the sample data with a 0.05 significance level to test the claim that for the population of ages of best actresses and best actors, the differences have a mean less than 0 (indicating that the best actresses are generally younger than best actors). in this example, mu subscript d is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the actress's age minus the actor's age. what are the null and alternative hypotheses for the hypothesis test?

Submarines control how much they float or sink in the ocean by changing the volume of air and water contained in large ballast tanks. when the tanks are completely full of water, the submarine increases its overall mass and sinks down to the bottom. when the tanks are completely full of air, the submarine reduces its overall mass and floats to the surface. depending on the density of the seawater surrounding the submarine, it will pump seawater in or out of the tanks in order to achieve the same overall density as the sea water and float neutrally in the water. the volume of the submarine never changes. when the tanks are completely full of water, a submarine with a volume of 7.8\times10^3\text{ m}^37.8×10 3 m 3 7, point, 8, times, 10, start superscript, 3, end superscript, space, m, start superscript, 3, end superscript has a total mass of 8\times10^6\text{ kg}8×10 6 kg8, times, 10, start superscript, 6, end superscript, space, k, g. the density of the seawater is 10^3\text{ kg/m}^310 3 kg/m 3 10, start superscript, 3, end superscript, space, k, g, slash, m, start superscript, 3, end superscript. to make that submarine float neutrally, and neither float nor sink in the ocean, what volume of water does that submarine need to subtract from its tanks?