For each of the following scenarios, identify: the population of interest, the outcome variable being measured on each observational unit, whether the outcome variable being measured is categorical or quantitative/Continuous, the parameter of interest, define both in words and using the appropriate statistical symbol (π, π1 -π2, µ, µ1 - µ2, or µd), and the null and alternative hypotheses, written in correct statistical notation (not in words) Name the hypothesis test you would use. For example, some tests we have learned are: one sample t-test of the population mean one sample z-test of the population proportion independent two-sample pooled t-test for the difference between population means independent two-sample unpooled z-test for the difference between population means Paired t-test for 2 dependent samples independent two-sample z-test for the difference between population proportions a) Suppose from large studies we know that the mean cholesterol in children aged 2-14 is 175 mg/dL. We wish to see if there is a familial aggregation of cholesterol level. We identify a group of fathers who have elevated cholesterol levels (>250 mg/dL) and have had a heart attack and measure the cholesterol levels of their offspring within the 2-14 age range.

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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For each of the following scenarios, identify:

the population of interest,
the outcome variable being measured on each observational unit,
whether the outcome variable being measured is categorical or quantitative/Continuous,
the parameter of interest, define both in words and using the appropriate statistical symbol (π, π1 -π2, µ, µ1 - µ2, or µd), and
the null and alternative hypotheses, written in correct statistical notation (not in words)

Name the hypothesis test you would use. For example, some tests we have learned are:

one sample t-test of the population mean
one sample z-test of the population proportion
independent two-sample pooled t-test for the difference between population means
independent two-sample unpooled z-test for the difference between population means
Paired t-test for 2 dependent samples
independent two-sample z-test for the difference between population proportions

a) Suppose from large studies we know that the mean cholesterol in children aged 2-14 is 175 mg/dL. We wish to see if there is a familial aggregation of cholesterol level. We identify a group of fathers who have elevated cholesterol levels (>250 mg/dL) and have had a heart attack and measure the cholesterol levels of their offspring within the 2-14 age range.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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