Answered: Consider four possible combinations of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Consider four possible combinations of sample size and treatment assignment rules.

n=50, treatment assigned to those below the median height (i.e. shortest 50%)
n=500, treatment assigned to those below the median height (i.e. shortest 50%)
n=50, treatment randomly assigned to 50% of the sample.
n=500, treatment randomly assigned to 50% of the sample.

To simulate the class example with realistic data, I drew a random sample of people from a much larger dataset from the CDC that measures height and weight of individuals among other things. For each sample, I added 20 lbs to the weights of the individuals that were assigned to the treatment group and did nothing to the weights of the control group. I then calculated the average weight for each group and calculated the treatment-control difference.

The graph below plots the treatment-control difference with 95% confidence intervals for the four scenarios in no particular order.

Which estimates correspond to which scenario?

Which estimates are statistically significant at the 5% level?

Would you rather be in Scenario A or Scenario B?

There is nothing else for these questions.

Estimating the Weight of a 20 Ibs Cat
Avg Effect Estimates under Different Conditions
А-
B-
C-
D
-60
-40
-20
40
60
Ibs
20

DIFFERENCE IN GROUP MEANS
Average Weight by Group
Average Weight by Group
Random Assignment
Assigned to Below Median Height
187.009
187.664
174.548
169.868
Control Group (No Cat)
Treatment Group (Cat)
Control Group (No Cat)
Treatment Group (Cat)
Treatment-Control Difference: – 12.5 lbs
Treatment-Control Difference: 17.8 Ibs
Avg Treatment Effect + Selection Bias + Chance Differences
Avg Treatment Effect + Chance Differences
007
01
mean of scaleweight
007
09
mean of scaleweight

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

Expert Solution

Step 1 of 2: Explanation

Decision based Confidence interval:

If zero includes in the confidence interval, we fail to reject Null hypothesis at 5% level
If zero does not includes in the confidence interval, we reject Null hypothesis at 5% level

Width of the Confidence interval: