Question

THIS IS NOT MEANT TO BE A SAMPLE TEST. EXAM QUESTIONS MAY NOT BE SIMILAR TO THOSE IN THIS REVIEW.

1. Read the values of the variable VOL in the dataset IQandBrainSize and find the proportion of sample values within 1, 2 and 3 sample standard deviations from the mean.

2. Nucryst Pharmaceutical, Inc. announced the results of its first human trial of NPI 32101, a topical form of its skin ointment. A total of 225 patients diagnosed with skin irritations were randomly divided into three groups as part of a double-blind, placebo-controlled study to test the effectiveness of the new topical cream. The first group received a 0.5% cream, the second group received a 1.0% cream, and the third group received a placebo. Groups were treated twice daily for a 6-week period.

1. Is this an observational study?

2. What are the treatments?

3. What does it mean for this study to be double-blind?

4. What is the control group for this study?

5. Identify the experimental units.

3. You have in R a data set dat consisting of persons’ names. Issue R commands to obtain a sample of size 100 from this population consisting of all the names other than “Aron”.

4. Consider a random sample of coins and record the year stamped on each. Would you expect the distribution of numbers to be symmetric or skewed? Why?

5.  A sample consists of seven points. Explain how to add one more item to the sample so that the median doesn’t change.

6. A uniform distribution takes values between 1 and 4. Draw the density. Show the scales on both axes.

7. Find the 90th percentile of a normal distribution with mean 23 and standard deviation 7.

8. You roll 4 dice. What is the probability of getting at least one 6?

9. These are the distributions of blood types in the US and Ireland. Choose one person in each country independently. What is the probability that they have the same blood type?

Blood Type	A	B	AB	O
U. S.	.42	.11	.03	.44
Ireland	.35	.10	.03	.52

10. You toss two balanced coins independently. Let A be the event head on the first toss and let B be the event both tosses have the same outcome. Compute P(A), P(B), P(B|A). Are A, B independent?

11. A data set has Q1 = 54.5 and Q3 = 200. What values will be considered outliers?

12. When should relative frequencies be used when comparing two data sets? Why?

13. Describe the circumstances in which a bar graph is preferable to a pie chart. When is a pie chart preferred over a bar graph?

Answer 1

7)

µ=   23                  
σ =    7                  
P(X≤x) =   0.9000                  
                      
Z value at    0.9   =   1.2816   (excel formula =NORMSINV(   0.9   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   1.282   *   7   +   23  
X   =   31.9709   (answer)          

90th percentile = 31.97

8)

P(at least one 6) = 1-P(no six) = 1 - (5/6)^4 = 0.5177

9)

Blood Type	A	B	AB	O
U. S.	.42	.11	.03	.44
Ireland	.35	.10	.03	.52

P(same blood type) = .42*.35+.11*.1+.03*.03+.44*.52 = 0.3877

10)

P(A) = 1/2

P(B) = P(HH,TT) = 2/4 = 1/2

P(B|A) = 1/2

yes, A nd B are independent because P(A|B) = P(A)

11)

IQR = Q3-Q1 =    200-54.5=   145.5
      
1.5IQR =    218.25  
      
lower bound=Q1-1.5IQR=   -163.75  
upper bound=Q3+1.5IQR=   418.25  
      
      
outlier =values outside lower bound and upper bound