Note : Please solve using MS office Suppose we want to compare the average yearly income in Providence and Boston, two neighboring cities in New England. It is known from experience that the variance of yearly incomes in Providence is $40000 and the variance for yearly incomes in Boston is $90000. A random sample of 40 families was taken in Providence, yielding a mean yearly income of $47000, while a random sample of 30 families was taken in Boston, yielding a mean yearly income of $52000. At α = .01 significance level, can it be concluded that the average yearly income in providence is more than the average yearly income in Boston?
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.
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Suppose we want to compare the average yearly income in Providence and Boston, two neighboring cities in New England. It is known from experience that the variance of yearly incomes in Providence is $40000 and the variance for yearly incomes in Boston is $90000. A random sample of 40 families was taken in Providence, yielding a mean yearly income of
$47000, while a random sample of 30 families was taken in Boston, yielding a mean yearly income of $52000. At α = .01 significance level, can it be concluded that the average yearly income in providence is more than the average yearly income in Boston?
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