Data on salaries in the public school system are published annually by a teachers' association The mean annual salary of (public) classroom teachers is $58 6 thousand Assume a standard deviation of $9 2 thousand Complete parts (a) through (e) below Determine the sampling distribution of the sample mean for samples of size 64 The mean of the sample mean is x $enter your response here (Type an integer or a decimal Do not round ) Part 2 The standard deviation of the sample mean is x $enter your response here (Type an integer or a decimal Do not round ) Part 3 b Determine the sampling distribution of the sample mean for samples of size 256 The mean of the sample mean is x $enter your response here (Type an integer or a decimal Do not round ) Part 4 The standard deviation of the sample mean is x $enter your response here (Type an integer or a decimal Do not round ) Part 5 c Do you need to assume that classroom teacher salaries are normally distributed to answer parts (a) and (b) Explain your answer A No, because if x is normally distributed, then x must be normally distributed B Yes, because x is only normally distributed if x is normally distributed C Yes, because the sample sizes are not sufficiently large so that x will be approximately normally distributed, regardless of the distribution of x D No, because the sample sizes are sufficiently large so that x will be approximately normally distributed, regardless of the distribution of x Part 6 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 enter your response here (Round to three decimal places as needed ) Part 7 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 enter your response here (Round to three decimal places as needed )

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Question: Data on salaries in the public school system are published annually by a teachers' association. The mean annual salary of (public) classroom teachers is $58.6

Data on salaries in the public school system are published annually by a teachers' association. The mean annual salary of (public) classroom teachers is $58.6 thousand. Assume a standard deviation of $9.2 thousand. Complete parts (a) through (e) below. Determine the sampling distribution of the sample mean for samples of size 64.

The mean of the sample mean is

x=$enter your response here.

(Type an integer or a decimal. Do not round.)

Part 2

The standard deviation of the sample mean is

x=$enter your response here.

(Type an integer or a decimal. Do not round.)

Part 3

b. Determine the sampling distribution of the sample mean for samples of size 256.

The mean of the sample mean is

x=$enter your response here.

(Type an integer or a decimal. Do not round.)

Part 4

The standard deviation of the sample mean is

x=$enter your response here.

(Type an integer or a decimal. Do not round.)

Part 5

c. Do you need to assume that classroom teacher salaries are normally distributed to answer parts (a) and (b)? Explain your answer.

No, because if x is normally distributed, then x must be normally distributed.

B.Yes, because x is only normally distributed if x is normally distributed.

C.Yes, because the sample sizes are not sufficiently large so that x will be approximately normally distributed, regardless of the distribution of x.

D.No, because the sample sizes are sufficiently large so that x will be approximately normally distributed, regardless of the distribution of x.

Part 6

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? enter your response here

(Round to three decimal places as needed.)

Part 7

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? enter your response here

(Round to three decimal places as needed.)

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