Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and the alcohol content of each bottle is determined. let denote the average alcohol content for the population of all bottles of the brand under study. suppose that the resulting 95% confidence interval is (7.8, 9.4).
a) would a 90% confidence interval calculated from this same sample have been narrower or wider than the given interval? explain your reasoning.
b) consider the following statement: there is a 95% chance that mu is between 7.8 and 9.4. is this statement correct? why or why not?
c) consider the following statement: we can be highly confident that 95% of all bottles of this type of cough syrup have an alcohol content that is between 7.8 and 9.4. is this statement correct? why or why not?
d) consider the following statement: if the process of selecting a sample of size 50 and then computing the corresponding 95% interval is repeated 100 times, 95 of the resulting intervals will include mu. is this statement correct? why or why not?

Which expression is equivalent to (3^2)^-2 a.-81 b.-12 c.1/81 d.1/12

If a and −a are numbers on the number line, which expression must give the distance between them? a) 0 b) a c) |2a| d) |a|

(i really need ) read the story problem, and then answer the questions that follow. gordon works for a graphic design firm and is creating a label for a food truck vendor. the vendor specializes in finger food and wants to sell food in right conical containers so that they are easy for people to hold. to complete his label, gordon needs to collect several different measurements to ensure that the label he designs will fit the surface of the container. gordon has been told that the containers have a diameter of 4 inches and a height of 6 inches. part a: find the slant height of the cone. the slant height is the distance from the apex, or tip, to the base along the cone’s lateral surface. show your work. part b: find the measure of the angle formed between the base of the cone and a line segment that represents the slant height. part c: imagine two line segments where each represents a slant height of the cone. the segments are on opposite sides of the cone and meet at the apex. find the measurement of the angle formed between the line segments.