In the advertisements for a large university, the dean of the School of Business claims that the average salary of the school’s graduates one year after graduation is $770 per week with a standard deviation of $100.A second-year student in the business school who has just completed his statistics course would like to check whether the claim about the mean is correct.He does a survey of 25 people who graduated one year ago and determines their weekly salary.He discovers the sample mean to be $750.To interpret his finding, he needs to calculate the probability that a sample of 25 graduates would have a mean of $750 or less when the population mean is $800 and the standard deviation is $100.To rebut the dean's claim, he needs to find out P (sample mean is less than 770) P (sample mean is less than 750) P (sample mean is less than 800) P (sample mean is greater than 770)

Given that Sample size (n)=25 Sample mean =$750 Population mean =800 calculate the probability that a sample of 25 graduates would have a mean of $750 or less we have to find Solution: To calculate the probability that a sample of 25 graduates would have a mean of $750 or less we have to find P (sample mean is less than 750) =P( x̄<750 ) Hence option (b) is correct.... P (sample mean is less than 750)

Answered: To interpret his finding, he needs to…

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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In the advertisements for a large university, the dean of the School of Business claims that the average salary of the school’s graduates one year after graduation is $770 per week with a standard deviation of $100.

A second-year student in the business school who has just completed his statistics course would like to check whether the claim about the mean is correct.

He does a survey of 25 people who graduated one year ago and determines their weekly salary.

He discovers the sample mean to be $750.

To interpret his finding, he needs to calculate the probability that a sample of 25 graduates would have a mean of $750 or less when the population mean is $800 and the standard deviation is $100.

To rebut the dean's claim, he needs to find out

P (sample mean is less than 770)

P (sample mean is less than 750)

P (sample mean is less than 800)

P (sample mean is greater than 770)

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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