Data on salaries in the public school system are published annually by a teachers' association. The mean annual salary of (public) classroom teachers is $55.1 thousand. Assume a standard deviation of $9.2 thousand. Complete parts (a) through (e) below.Please solve all the parts correctly. a. Determine the sampling distribution of the sample mean for samples of size 64.The mean of the sample mean is µ = $ 56.3. (Type an integer or a decimal. Do not round.)The standard deviation of the sample mean is; =S.95. (Type an integer or a decimal. Do not round.)b. Determine the sampling distribution of the sample mean for samples of size 256.The mean of the sample mean is µ; = $ 56.3. Type an integer or a decimal. Do not round.)The standard deviation of the sample mean is o; =S .475|. (Type an integer or a decimal. Do not round.)c. Do you need to assume that classroom teacher salaries are normally distributed to answer parts (a) and (b)? Explain your answer.O A. Yes, because x is only normally distributed if x is normally distributed.O B. No, because the sample sizes are sufficiently large so that x will be approximately normally distributed, regardless of the distribution of x.O C. Yes, because the sample sizes are not sufficiently large so that x will be approximately normally distributed, regardless of the distribution of x.O D. No, because if x is normally distributed, then x must be normally distributed.d. What is the probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 64classroom teachers will be at most $1000?e. What is the probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 256classroom teachers will be at most $1000?(Round to three decimal places as needed.)

We have given that Population mean = 55.1 Population standard deviation = 9.2 Sample mean =…

Answered: Data on salaries in the public school…

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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Data on salaries in the public school system are published annually by a teachers' association. The mean annual salary of (public) classroom teachers is $55.1 thousand. Assume a standard deviation of $9.2 thousand. Complete parts (a) through (e) below.

Please solve all the parts correctly.

a. Determine the sampling distribution of the sample mean for samples of size 64.
The mean of the sample mean is µ = $ 56.3. (Type an integer or a decimal. Do not round.)
The standard deviation of the sample mean is; =S.95. (Type an integer or a decimal. Do not round.)
b. Determine the sampling distribution of the sample mean for samples of size 256.
The mean of the sample mean is µ; = $ 56.3. Type an integer or a decimal. Do not round.)
The standard deviation of the sample mean is o; =S .475|. (Type an integer or a decimal. Do not round.)
c. Do you need to assume that classroom teacher salaries are normally distributed to answer parts (a) and (b)? Explain your answer.
O A. Yes, because x is only normally distributed if x is normally distributed.
O B. No, because the sample sizes are sufficiently large so that x will be approximately normally distributed, regardless of the distribution of x.
O C. Yes, because the sample sizes are not sufficiently large so that x will be approximately normally distributed, regardless of the distribution of x.
O D. No, because if x is normally distributed, then x must be normally distributed.
d. What is the probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 64
classroom teachers will be at most $1000?
e. What is the probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 256
classroom teachers will be at most $1000?
(Round to three decimal places as needed.)

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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