Category: Mathematics and Statistics : Mathematics

Consider an unbalanced study with six subjects, identified as A, B, C, D, E and G. In the actual study, • Subjects A and B are assigned to the first treatment, and the other subjects are assigned to the second treatment. • There are exactly two successes, obtained by A and C. This information is needed for parts (a)–(c) below. (a) Compute the observed value of the test statistic. (b) Assume that the Skeptic is correct. Determine the observed value of the test statistic for the assignment that places D and E on the first treatment, and the remaining subjects on the second treatment. (c) We have obtained the sampling distribution of the test statistic on the assumption that the Skeptic is correct. It also is possible to obtain a sampling distribution of the test statistic if the Skeptic is wrong provided we specify exactly how the Skeptic is in error. These new sampling distributions are used in the study of statistical power which is briefly described in Chapter 7 of the text. Assume that the Skeptic is correct about subjects A and G, but incorrect about subjects B, C, D and E. For the assignment that puts D and G on the first treatment, and the other subjects on the second treatment, determine the response for each of the six subjects.

A sample of size 40 yields the following sorted data. Note that I have x-ed out x(39) (the second largest number).
This fact will NOT prevent you from answering the questions below. 14.1 46.0 49.3 53.0 54.2 54.7 54.7 54.7 54.8 55.4 57.6 58.2 58.3 58.7 58.9 60.8 60.9 61.0 61.1 63.0 64.3 65.6 66.3 66.6 67.0 67.9 70.1 70.3 72.1 72.4 72.9 73.5 74.2 75.3 75.4 75.9 76.5 77.0 x 88
(a) Calculate range, IQR, and median of these data
. (b) Given that the mean of these data is 63.50 (exactly) and the standard deviation is 12.33, what proportion of the data lie within one standard deviation of the mean?

1 )Outliers & Missing Data: Answer the following questions:
a. True or False: Non-random missing data are often times more problematic than random missing data.
b. True or False: A normal practice of dealing with missing data is to eliminate them regardless of the amount as they can introduce severe bias into the results. 
c. Use Outlier.sav and identify potential outliers. Provide the reasons of such identification. [Hint: A boxplot might help]
d. Given the sample size in Outlier.sav, what seems to be the most appropriate remedy for the outliers?
3 Scholarly references

Starting from an airport, an airplane flies 225 miles northwest, then 150 miles south-west.
Answer the following:
Draw a graph or figure to represent this situation.
Describe how the concepts of vectors and complex plane can be applied in this case.
How far, in miles, from the airport is the plane?
Provide another example of a scenario that involves the same concept.
Note: When drawing the diagram, try to be as consistent as possible.
That is, when drawing the vector for length 225 miles, make this line about 1.5 times longer than the vector representing 150 miles.
When there is a reference to “northwest” this means to draw a vector to the left of north, where the angle between the vector and the vertical axis is 45 degrees.

Starting from an airport, an airplane flies 225 miles northwest, then 150 miles south-west.
Answer the following:
Draw a graph or figure to represent this situation.
Describe how the concepts of vectors and complex plane can be applied in this case.
How far, in miles, from the airport is the plane?
Provide another example of a scenario that involves the same concept.
Note: When drawing the diagram, try to be as consistent as possible.
That is, when drawing the vector for length 225 miles, make this line about 1.5 times longer than the vector representing 150 miles.
When there is a reference to “northwest” this means to draw a vector to the left of north, where the angle between the vector and the vertical axis is 45 degrees.