1) A researcher studied whether pregnant women who consumed more than 800 mg of caffeine per day had babies with a lower birth weight (in lbs)

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1) A researcher studied whether pregnant women who consumed more than 800 mg of caffeine per day had babies with a lower birth weight (in lbs). The results are in the table below:

Caffeinated women's babies weights

7.5

6.7

5.2

6.8

7.4

7.7

5.6

6.9

Non-caffeinated women's babies weights

7.8

7.6

8.1

7.5

7.1

7.2

7.9

Test to determine if the use of caffeine lowered birth weights using α = 0.05.

2) You intend to poll students in order to determine the proportion of all students who voted in an election. What sample size do you need to choose to ensure that the margin of error is less than 3% assuming a 90% level of confidence? Hint: "To ensure" means that, even in the worst case scenario which is when the variation is largest, your confidence interval would still have a 90% chance of containing the true proportion of all students.