A study of Vitamin D levels compared the blood concentration of Vitamin

D in nanograms per milliliter for residents of Kenya and residents of

Finland. The following summary values were calculated from each

random sample of participants:



Kenya Finland



Mean Vitamin D

Blood

Concentration

(ng/ml)



μK = 37.1



Mean Vitamin D

Blood

Concentration



μF = 33.8



Standard

Deviation σK = 3.75 Standard



Deviation σK = 5.15

Sample Size nK = 55 Sample Size nK = 43



Part A. Explain why a paired t-test is not an appropriate procedure to analyze these data. (4

points)

Part B: Conduct a complete hypothesis test to determine whether there is a difference at the

5% significance level between the mean blood concentration of Vitamin D between

residents of Kenya and residents of Finland. Be sure to state your hypotheses, check all

conditions, show all calculations, and report your conclusions, all in the context of the

problem. (16 points)

1. Are the proportions of girls who take advanced STEM courses consistent between private
   

and public schools? To investigate this claim, researchers examined all girls’ enrollment

records from randomly-selected private schools and randomly-selected public schools

across the country. They found that 18% of 2510 girls enrolled in the private schools take

advanced STEM courses compared to 15% of the 3292 girls enrolled in public schools. You

may assume that observations are independent.

Part A. What is the sampling technique used in this study? How do you know? (2 points)

Part B. Is this an observational study or an experiment? Explain. (2 points)

Part C. Does this data provide convincing evidence, at the 1% significance level, that there is

a greater proportion of girls who enroll in advanced STEM courses at private schools than

public schools? Conduct a complete hypothesis test. (16 points)