Income Tax and the IRS. In 2010, the Internal Revenue Service (IRS) sampled 308,946 tax returns to obtain estimates of various parameters. Data were published in Statistics of Income, Individual Income Tax Returns. According to that document, the mean income tax per return for the returns sampled was $11,266. a. Explain the meaning of sampling error in this context.b. If, in reality, the population mean income tax per return in 2010 was $11,354, how much sampling error was made in estimating that parameter by the sample mean of $11,266?c. If the IRS had sampled 400,000 returns instead of 308,946, would the sampling error necessarily have been smaller? Explain your answer.d. In future surveys, how can the IRS increase the likelihood of small sampling error?
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.
Income Tax and the IRS. In 2010, the Internal Revenue Service (IRS) sampled 308,946 tax returns to obtain estimates of various parameters. Data were published in Statistics of Income, Individual Income Tax Returns. According to that document, the
a. Explain the meaning of sampling error in this context.
b. If, in reality, the population mean income tax per return in 2010 was $11,354, how much sampling error was made in estimating that parameter by the sample mean of $11,266?
c. If the IRS had sampled 400,000 returns instead of 308,946, would the sampling error necessarily have been smaller? Explain your answer.
d. In future surveys, how can the IRS increase the likelihood of small sampling error?
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