Nikita is a government official looking to find evidence on whether the mean taxable income for an individual taxpayer in the region dropped since the previous year. She surveyed 32 individual taxpayers in the region and found the taxable income of each individual as shown in the data set provided. Instead of using the standard deviation from the survey, Nikita decided to use the census data for the region to assume that the population standard deviation of income is $26,744. The mean taxable income in the region was $62,712 for the previous year. (a) H0:μ=$62,712;Ha:μ<$62,712, which is a left-tailed test. (b) Taxable income of each individual is given below. Use Excel to test whether this year's mean taxable income for an individual taxpayer in the region is less than the mean taxable income from the previous year, and then draw a conclusion in the context of the problem, where α=0.10. Calculate the test statistic, z, rounding to two decimal places, and the p-value, rounding to three decimal places. Taxable income ($) 12193 64586 60363 59639 103402 24127 53641 38963 78596 49328 33983 64023 49771 89073 59433 21930 53789 30236 41639 87935 73396 69640 69371 104896 112354 96396 83921 72539 52186 91483 32069 17296

Name: Nikita is a government official looking to find evidence on whether th
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Description: Nikita is a government official looking to find evidence on whether the mean taxable income for an individual taxpayer in the region dropped since the previous year. She surveyed 32 individual taxpayers in the region and found the taxable income of e

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Nikita is a government official looking to find evidence on whether the mean taxable income for an individual taxpayer in the region dropped since the previous year. She surveyed 32 individual taxpayers in the region and found the taxable income of each individual as shown in the data set provided. Instead of using the standard deviation from the survey, Nikita decided to use the census data for the region to assume that the population standard deviation of income is $26,744. The mean taxable income in the region was $62,712 for the previous year.

(a) H0:μ=$62,712;Ha:μ<$62,712, which is a left-tailed test.

(b) Taxable income of each individual is given below.

Use Excel to test whether this year's mean taxable income for an individual taxpayer in the region is less than the mean taxable income from the previous year, and then draw a conclusion in the context of the problem, where α=0.10. Calculate the test statistic, z, rounding to two decimal places, and the p-value, rounding to three decimal places. Taxable income ($)

12193

64586

60363

59639

103402

24127

53641

38963

78596

49328

33983

64023

49771

89073

59433

21930

53789

30236

41639

87935

73396

69640

69371

104896

112354

96396

83921

72539

52186

91483

32069

17296

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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