# Question

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.

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.

## Answer to relevant Questions

B. Ciochetti et al. studied mortgage loans in the article "A Proportional Hazards Model of Commercial Mortgage Default with Originator Bias" (Journal of Real Estate and Economics, Vol. 27, No. 1, pp. 5-23). According to the ...Calcium is the most abundant mineral in the human body and has several important functions. Most body calcium is stored in the bones and teeth, where it functions to support their structure. Recommendations for calcium are ...In Example 7.9 on page 294, we conducted a simulation to check the plausibility of the central limit theorem. The variable under consideration there is household size, and the population consists of all U.S. households. A ...The American Council of Life Insurers provides information about life insurance in force per covered family in the Life Insurers Fact Book. Assume that the standard deviation of life insurance in force is $50,900. a. ...The following table gives the monthly salaries (in $1000s) of the six officers of a company. a. Calculate the population mean monthly salary, μ. There are 15 possible samples of size 4 from the population of six officers. ...Post your question

0