Answered: Salaries for teachers in a particular…

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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Hello, I am struggling with a few questions on my homework. If you could answer the questions and explain how/why you got that answer I would greatly appreciate it. Thank you!

Question 1: Salaries for teachers in a particular state have a mean of $42,000 and a standard deviation of $6,600.

a. If we randomly select 19 teachers from that district, can you determine the sampling distribution of the sample mean? If yes, what is the name of the distribution, what is the mean, and the standard error?

b. If we randomly select 65 teachers from that district, can you determine the sampling distribution of the sample mean? If yes, what is the name of the distribution, what is the mean, and the standard error?

c. What sample size (65 or 19) would be needed to know the population distribution of teacher salaries is normal in order to answer? (*Would it just be 19 because it is less than 30 and therefore considered to be small? I know that generally anything greater than or equal to 30 is considered normally distributed when using random selection.)

d. Assuming a sample size of 65, what is the probability that the sampling error is within $1,000 of the true mean?

e. Assuming a sample size of 65, what is the 90^th percentile for the AVERAGE teacher’s salary?

f. Assuming that teacher’s salaries are normally distributed, what is the 90^th percentile for an INDIVIDUAL teacher’s salary?

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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