Problem 5: Please answer parts a, b, and c! A current area of research interest is the familial aggregation of cardiovascular risk factors in general, and lipid levels in particular. Suppose that it is known that the national average cholesterol level in children is 175 mg/dL. A group of men who have died from heart disease within the past year are identified, and the cholesterol levels of 57 of their offspring are measured. The average cholesterol level of the offspring is found to be 181.5 mg/dL with standard deviation 29.8 mg/dL. At α = .06, can it be concluded that the average cholesterol level of children whose father died from heart disease is higher than the national average? (a) Find the value of the test statistic for the above hypothesis.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Problem 5: Please answer parts a, b, and c!
A current area of research interest is the familial aggregation of cardiovascular risk factors in general, and lipid levels in particular. Suppose that it is known that the national average cholesterol level in children is 175 mg/dL. A group of men who have died from heart disease within the past year are identified, and the cholesterol levels of 57 of their offspring are measured. The average cholesterol level of the offspring is found to be 181.5 mg/dL with standard deviation 29.8 mg/dL. At α = .06, can it be concluded that the average cholesterol level of children whose father died from heart disease is higher than the national average? |
(a) | Find the value of the test statistic for the above hypothesis. |
(b) | Find the critical value. |
(c) | Find the p-value. |
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