Q 1. According to a Boston Globe story, only about 1 in 6 Americans have blue eyes, whereas in 1900 about half had blue eyes. (Source:Data from The Boston Globe October 17, 2006.) a. For a random sample of 100 living Americans, find the mean and standard deviation of the proportion that have blue eyes. b. In a course you are taking with 100 students, half of the students have blue eyes. Would this have been a surprising result if the sample were a random sample of Americans? Answer by finding how many standard deviations that sample result falls from the mean of the sampling distribution of the proportion of 100 students who have blue eyes. c. In part b, identify the population distribution, the data distribution, and the sampling distribution of the sample proportion.
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.
Q 1.
According to a Boston Globe story, only about 1 in 6 Americans have blue eyes, whereas in 1900 about half had blue eyes. (Source:Data from The Boston Globe October 17, 2006.)
a. For a random sample of 100 living Americans, find the mean and standard deviation of the proportion that have blue eyes.
b. In a course you are taking with 100 students, half of the students have blue eyes. Would this have been a surprising result if the sample were a random sample of Americans? Answer by finding how many standard deviations that sample result falls from the mean of the sampling distribution of the proportion of 100 students who have blue eyes.
c. In part b, identify the population distribution, the data distribution, and the sampling distribution of the sample proportion.
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