In the article "coffee, caffeine, and risk of depression among women" in the september 2011 edition of the archives of internal medicine, researchers investigated the relationship between caffeine consumption and depression among women.

the participants in this study were older, with substantially lower rates of depression when compared to female teens. researchers compared two groups of women (among others) in this study: those who do not drink coffee and those who routinely drink 4 or more cups of coffee each day.

for the following question, a coffee drinker is a woman who drinks four or more cups each day.

suppose that the difference between the proportions of coffee drinkers and non-coffee drinkers who are depressed is equal to −0.02. (so the statistic is p-hat for coffee drinkers minus p-hat for non-coffee drinkers.)

which group has a higher depression rate?

a) coffee drinkers

b) non-coffee drinkers

Thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 127 millimeters, and a variance of 36. if a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.5 millimeters? round your answer to four decimal places.

The length of the line segment joining the midpoints of sides ab and bc of the parallelogram abcd is 10. find the length of diagnol ac

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