Programming Homework Help

1.It is thought that an enzyme level has a T-distribution with variance 1.2 and mean 0.
What’s the probability the enzyme level lies within one standard deviation of its mean?

2. Another enzyme level has a lognormal distribution with μ=1 and σ=1. About 5,000
hospitals measure this enzyme level for at least 10,000 patients (i.e., sample size).
Estimate the standard deviation of the mean and median enzyme level, respectively.

3. A blood test is done on two groups (A & B) of people. The results are shown in the
Table. Are the means of the two groups different?
A 51.8 52 50.6 53.4 53.8 50 50.2 51.2 50.8 51.4 49.2 50.6 52.4 54 51 53.2 50.4 51.8
B 46.6 40.8 57.6 48.2 52.6 47.6 50.2 48.6 43.8 56.6 48.8 46.8

4. Use Group A data in the Table above and find the standard deviation of its median (this
problem has nothing to do with the prior problem; you are just using Group A data)?

5. Two groups of people, C & D, have a dangerous disease. A new vaccine is given only to
C. In C, 140 persons recovered and 27 did not. In D, 438 recovered and 228 did not. Is
the vaccine effective?

6. 250 parents, each with 3 kids, are sampled and the number of daughters they have is
shown in the Table. Do you think the chances of the birth of a boy or girl is 50-50?
Possible count of daughters 0 girls 1 girl 2 girls 3 girls
Observed count 24 108 95 23

7. To test the hypothesis (H0) that a coin is fair, the following rule is adopted: if the number
of heads in 64 tosses of the coin lies between 28 and 36, the coin is fair; otherwise not.
Find the probability of rejecting H0 when it is actually correct. Draw the OC curve.

8. You are given XY19_midterm_2021.csv where Y has been “put together” using some of
the Xs. Use linear/ridge regression to model Y.