Out: 04/15 19:00
Due: 04/29 19:00
Collaboration:
Collaboration on solving the assignment is allowed, after you have thought about the problem sets on your own. It is also OK to get clarification (but not solutions) from online resources, again after you have thought about the problem sets on your own. There are two requirements:
Cite your collaborators fully and completely (e.g., “XXX explained to me what is asked in problem set 3”). Or cite online resources (e.g., “I got inspired by reading XXX”) that helped you.
Write your scripts and report independently - the scripts and report must come from you only.
Submitting your assignment:
Submit your R scripts and report to TA (12332275@mail.sustech.edu.cn)
Late Submission:
Late submissions will not receive any credit.
Hint: Please follow the general steps of hypothesis testing as introduced in the lecture.
Toss a dice 300 times repeatedly, frequency of number
1 to 6 is as follows：
40, 70, 48, 60, 52, 30
[10 points] Based on the observations, is this a fair dice?
An experiment is conducted to study the relationship between aerosol surface density (m-1) and Pb content. The observations are as fellow:
Surface density:
8.7, 8.5, 9.1, 9.3, 6.3, 7.8, 9.9, 6.5, 6.6, 9.5, 9.4, 7.2, 8.6, 9.6, 11.1
Pb content:
6.0, 5.7, 6.0, 5.7, 4.7, 5.5, 6.4, 4.2, 6.2, 5.9, 5.7, 5.7, 6.1, 6.3, 6.0
[10 points] Does aerosol surface density relate to Pb content? Report your results.
Exposure to a consistent level of noise may increase human’s blood
pressure. To test this, blood pressures are measured for 12
volunteers before and after noise exposure.
Before:
134, 112, 113, 113, 111, 153, 143, 105, 142, 157, 119, 111
After:
132, 126, 149, 124, 118, 157, 142, 124, 139, 157, 135, 125
[10 points] Do the observations support the hypothesis? Report your results.
Injecting antibiotics causes the phenomenon of antibiotics and plasma protein binding, which will reduce the efficacy of the drug.
The following is a list of the percentage of antibiotics bound to
plasma proteins when 5 antibiotics are injected into
cattle:
| Penicillin | Tetracycline | Streptomycin | Erythromycin | Chloramphenicol |
|---|---|---|---|---|
| 29.6 | 27.3 | 5.8 | 19.0 | 29.2 |
| 24.3 | 32.6 | 6.2 | 18.3 | 32.8 |
| 28.5 | 30.8 | 11.0 | 17.4 | 25.0 |
| 32.0 | 34.8 | 8.3 | 21.6 | 24.2 |
[5 points] 4.1 Are there any significant differences in the percentage of the five antibiotics bound to plasma proteins?
[5 points] 4.2 Calculate the 95%
confidence interval of the average of the percentage of 5
antibiotics bound to plasma protein.
[5 points] 4.3 Find the 95% confidence
interval of the mean difference between penicillin and streptomycin.
The lapse rate is the rate at which temperature drops as you
increase elevation. Some hardy students were interested in checking
empirically if the lapse rate of 9.8 degrees C
km-1 was accurate for their hiking.
To investigate, they grabbed their thermometers and their Huawei wrist altimeters and found the following data on their hike.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
|---|---|---|---|---|---|---|---|---|
| Elevation (m) | 180 | 305 | 381 | 488 | 549 | 640 | 762 | 883 |
| Temperature (degrees C) | 13.3 | 12.2 | 13.3 | 10.0 | 8.3 | 9.4 | 8.3 | 7.2 |
[15 points] Draw a scatter plot with regression
line, and investigate if the lapse rate is 9.8 degrees C
km-1.