7.69 Teacher Salaries. Data on salaries in the public school sys- tem are published annually in Ranking of the States and Estimates of School Statistics by the National Education Association. The mean annual salary of (public) classroom teachers is $55.4 thousand. As- sume a standard deviation of $9.2 thousand. Do the following tasks for the variable “annual salary" of classroom teachers. a. Determine the sampling distribution of the sample mean for sam- ples of size 64. Interpret your answer in terms of the distribution of all possible sample mean salaries for samples of 64 classroom teachers. b. Repeat part (a) for samples of size 256. c. Do you need to assume that classroom teacher salaries are normally distributed to answer parts (a) and (b)? Explain your answer.
7.69 Teacher Salaries. Data on salaries in the public school sys- tem are published annually in Ranking of the States and Estimates of School Statistics by the National Education Association. The mean annual salary of (public) classroom teachers is $55.4 thousand. As- sume a standard deviation of $9.2 thousand. Do the following tasks for the variable “annual salary" of classroom teachers. a. Determine the sampling distribution of the sample mean for sam- ples of size 64. Interpret your answer in terms of the distribution of all possible sample mean salaries for samples of 64 classroom teachers. b. Repeat part (a) for samples of size 256. c. Do you need to assume that classroom teacher salaries are normally distributed to answer parts (a) and (b)? Explain your answer.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Transcribed Image Text:7.69 Teacher Salaries. Data on salaries in the public school sys-
tem are published annually in Ranking of the States and Estimates of
School Statistics by the National Education Association. The mean
annual salary of (public) classroom teachers is $55.4 thousand. As-
sume a standard deviation of $9.2 thousand. Do the following tasks
for the variable "annual salary" of classroom teachers.
a. Determine the sampling distribution of the sample mean for sam-
ples of size 64. Interpret your answer in terms of the distribution
of all possible sample mean salaries for samples of 64 classroom
teachers.
b. Repeat part (a) for samples of size 256.
c. Do you need to assume that classroom teacher salaries are normally
distributed to answer parts (a) and (b)? Explain your answer.
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. Repeat part (d) for samples of size 256.
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