1) when would you carry out a t-test for independent means? how is this different from the situation in which you would carry out a t-test for dependent means?

2) for each of the following studies, say whether you would use a t-test for independent means or for dependent means.

an educational researcher randomly assigns a group of 47 fourth-grade students to receive a new after-school math program and 48 other fourth-grade students to receive the standard after-school math program, then measures how well they all do on a math test.

a. a marketing researcher measures 100 doctors’ reports of how many patients asked them about a particular drug the month before a major advertising campaign, and a month after the campaign.
b. a researcher tests the reaction time of a group of 14 individuals twice, once while in a very hot room and once while in a normal-temperature room.
c. a researcher measures the heights of 40 college students who are the firstborn in their families, then compares the 15 of them who come from a large family to the remaining 25 who come from smaller families.
d. a researcher tests performance on a math skills test among 250 individuals before and after they complete a one-day seminar on managing test anxiety.
e. a researcher compares the resting heart rate of 15 individuals who have been taking a particular drug to the resting heart rate of 48 individuals who have not been taking this drug.