Data on salaries in the public school system are published annually by a teacher
ID: 3063316 • Letter: D
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 $55.7 thousand. Assume a standard deviation of $7 2 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 -655 700 Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is%"(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 'SL .(Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o-Type an integer or a decimal. Do not round.) G. 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 xis only normally distributed if x is normally distributed. O B· Yes, because the sample sizes are not sufficiently large so that x wil be approximately normally distuted, regardiess of the distribution of OC. No, because the sample sizes are sufficiently large so that x will be approximately normally distributed, regardess 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?Explanation / Answer
Solution:- Given that = 55700 , = 7200
a) n = 64
=> x = 55700
=> x = 7200/sqrt(64) = 900
b) n = 256
=> x = 55700
=> x = 7200/sqrt(256) = 450
c. option C. No, because the sample sizes are sufficiently large so thatwill be approximately normallydistributed, regardless of the distribution of x.
d. P(|X - |<= 1000) = P(Z <= 1000/(7200/sqrt(64))
= P(-1.1111 < Z < 1.1111)
= 0.7330
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.