a. Determine the sampling distribution of the sample mean for samples of size 64. The mean of the sample mean is uç =s 56.3|. (Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o =$ .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 uç =s 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 $1000? (Round to three decimal places as needed.)
a. Determine the sampling distribution of the sample mean for samples of size 64. The mean of the sample mean is uç =s 56.3|. (Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o =$ .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 uç =s 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.)
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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Solve for all parts a-e for the question in the image below.
Transcribed Image Text: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.)
Transcribed Image Text:Data on salaries in the public school system are published annually by a teachers' association. The mean annual salary of (public) classroom teachers is $51.5 thousand. Assume a standard deviation of $7.6
thousand. Complete parts (a) through (e) below.
.....
a. Determine the sampling distribution of the sample mean for samples of size 64.
The mean of the sample mean is µ, = $ . (Type an integer or a decimal. Do not round.)
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