Answered: calculate the appropriate z scores.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 23PFA

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Question

1. Suppose that two graduating seniors, one a marketing major and one an accounting major, are comparing job offers. The accounting major has an offer for $55,000 per year, and the marketing student has an offer for $53,000 per year. Summary information about the distribution of offers is given below.

Accounting:	mean	=	56,000 standard deviation	=	1,200
Marketing:	mean	=	52,500 standard deviation	=	800

Then calculate the appropriate z scores. (Round your answers to two decimal places.)

accounting z score =

55,000 − 56,000

1,200

(so $55,000 is standard deviations below the mean)

marketing z score =

53,000 − 52,500

800

Relative to the appropriate data sets, the marketing offer is actually more attractive than the accounting offer (although this may not offer much solace to the marketing major).

Why is one of the z scores positive and the other one negative?

Because the means are different.

Because the standard deviations are different.

Because one of the values is greater than the mean and the other is less than the mean.

Because the values being compared are different.

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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