At western university the historical mean of scholarship examination scores for freshman applications is 900. a historical population standard deviation s = 175 is assumed known. each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.

a. state the hypotheses.

h0: µ =greater than or equal to 900, greater than 900, less than 900, etc?
ha: µ =greater than or equal to 900, greater than 900, less than 900, etc?

b. what is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean 935 (to the nearest whole number)?

c. use the confidence interval to conduct a hypothesis test. using a = .05, can the assistant dean conclude that the mean examination score for the new freshman applications has changed?

d. what is the p-value (to 3 decimals)?

Scarlet bought three pairs of sunglasses and two shirts for $81 and paula bought one pair of sunglasses and five shirts for $105 what is the cost of one pair of sunglasses and one shirt?

If square root x = -7, then x= -49 true or false

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24