Concept explainers
a.
Obtain the sampling distribution of mean
a.
Answer to Problem 8P
The sampling distribution of the mean
The sampling distribution of the mean
The sampling distribution of the mean
The sampling distribution of the mean
Explanation of Solution
It is given that 33% of taxpayers in the year 2010 with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for the given population of taxpayers is
The sampling distribution of the mean is approximately normal when the sample size is large regardless of the underlying distribution of the population from where it is taken.
The mean of the
In this context,
For the random sample of 30 taxpayers, the mean and standard deviation is calculated as,
Thus, for the random sample of 30 taxpayers with adjusted gross income between $30,000 and $60,000, the sampling distribution of the mean
For the random sample of 50 taxpayers, the mean and standard deviation is calculated as,
Thus, for the random sample of 50 taxpayers with adjusted gross income between $30,000 and $60,000, the sampling distribution of the mean
For the random sample of 100 taxpayers, the mean and standard deviation is calculated as,
Thus, for the random sample of 100 taxpayers with adjusted gross income between $30,000 and $60,000, the sampling distribution of the mean
For the random sample of 400 taxpayers, the mean and standard deviation is calculated as,
Thus, for the random sample of 400 taxpayers with adjusted gross income between $30,000 and $60,000, the sampling distribution of the mean
b.
Explain the advantage of using larger sample size.
b.
Explanation of Solution
From part (a), it can be observed that when sample size increases the standard error of the sample mean decreases.
Thus, larger sample reduces the standard error which results in a more accurate estimate of the population mean.
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Chapter 6 Solutions
Essentials of Business Analytics (MindTap Course List)
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt