The file “
pop2.csv” contains information associated to the blood pressure of an imaginary population of size 100,000. The file can be found on the internet (http://pluto.huji.ac.il/~msby/StatThink/Datasets/pop2.csv). The variables in this file are:
- id
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A numerical variable. A 7 digits number that serves as a unique identifier of the subject.
- sex
- age
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A numerical variable. The age of each subject.
- bmi
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A numerical variable. The body mass index of each subject.
- systolic
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A numerical variable. The systolic blood pressure of each subject.
- diastolic
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A numerical variable. The diastolic blood pressure of each subject.
- group
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A factor variable. The blood pressure category of each subject. The values are “
NORMAL” if both the systolic blood pressure is within its normal range (between 90 and 139) and the diastolic blood pressure is within its normal range (between 60 and 89). The value is “HIGH” if either measurements of blood pressure are above their normal upper limits and it is “LOW” if either measurements are below their normal lower limits.
Our goal in this question is to investigate the sampling distribution of the sample average of the variable “
bmi”. We assume a sample of size \(n=150\text{.}\)
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Compute the population average of the variable “
bmi”. -
Compute the population standard deviation of the variable “
bmi”. -
Compute the expectation of the sampling distribution for the sample average of the variable.
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Compute the standard deviation of the sampling distribution for the sample average of the variable.
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Identify, using simulations, the central region that contains 80% of the sampling distribution of the sample average.
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Identify, using the Central Limit Theorem, an approximation of the central region that contains 80% of the sampling distribution of the sample average.
