Part A) Suppose I wish to find the average intelligence quotient (IQ) of all Grade 5 children studying in local schools in United States. I first selected a simple random sample of 10 schools out of all local elementary schools in United States. Then I asked all the Grade 5 children in these chosen 10 schools to take an IQ test. Finally, I obtained the average value of all the IQ scores of children who took the test, which was 106. Which of the following statements is/are correct? I. The parameter in this study is the average IQ of all Grade 5 children who took the IQ test. II. Stratified sampling was employed in this study. a) Both (I) and (II) b) Only (I) c) Neither (I) nor (II) d) Only (II) Part B) A certain town has a population of 100,000, of which 20,000 are smokers and 80,000 are non-smokers. It is known that for the population, r(lung cancer | smoker) = 5% and r(lung cancer | non-smokers) = 1%. Suppose that 50% of lung cancer patients are chosen by simple random sampling, while 10% of residents without lung cancer are chosen by simple random sampling. By calculating r(lung cancer | smoker) in the sample using expected numbers, what can we say about U = sample r(lung cancer | smoker) and V = population r(lung cancer | smoker)? a) U = V b) U < V c) U > V
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Part A)
Suppose I wish to find the average intelligence quotient (IQ) of all Grade 5 children studying in local schools in United States. I first selected a simple random sample of 10 schools out of all local elementary schools in United States. Then I asked all the Grade 5 children in these chosen 10 schools to take an IQ test. Finally, I obtained the average value of all the IQ scores of children who took the test, which was 106. Which of the following statements is/are correct?
I. The parameter in this study is the average IQ of all Grade 5 children who took the IQ test.
II. Stratified sampling was employed in this study.
a) Both (I) and (II)
b) Only (I)
c) Neither (I) nor (II)
d) Only (II)
A certain town has a population of 100,000, of which 20,000 are smokers and 80,000 are non-smokers. It is known that for the population, r(lung cancer | smoker) = 5% and r(lung cancer | non-smokers) = 1%. Suppose that 50% of lung cancer patients are chosen by simple random sampling, while 10% of residents without lung cancer are chosen by simple random sampling. By calculating r(lung cancer | smoker) in the sample using expected numbers, what can we say about
U = sample r(lung cancer | smoker) and V = population r(lung cancer | smoker)?
a) U = V
b) U < V
c) U > V
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