2. The Ghana Revenue Authority (GRA) publishes annual figures on individual income tax returns in Statistics of Income, Individual Income Tax Returns. For the year 2009, the GRA reported that the mean tax of individual income tax returns was GHC 10,319. In actuality, the GRA reported the mean tax of a sample of 292,966 individual income tax returns from a total of more than 130 million such returns. a. Identify the population under consideration. b. Identify the variable under consideration. c. Is the mean tax reported by the GRA a sample mean or the population mean? d. Should we expect the mean tax x, of the 292,966 returns sampled by the GRA to be exactly the same as the mean tax, u, of all individual income tax returns for 2009? e. How can we answer questions about sampling error? For instance, is the sample mean tax T reported by the GRA likely to be within GHC 100 of the population mean tax, u?
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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