Data on salaries in the public school system are published annually in National Survey of Salaries and Wages in Public Schools by the Education Research Service. The mean annual salary of (public) classroom teachers is $49.0 thousand. Assume a standard deviation of $9.2 thousand.
Do the following for the variable "annual salary" of classroom teachers.
a. Determine the sampling distribution of the sample mean for samples 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.