Question

d The f te om Teachers is 553 thousand Data on alles in the public school systems are published by a bran parts (a) through ) below a. Determine the sampling distribution of the sample mean for sample of The mean of the sample meanis 5 (Type an integradacina De S standard of Care ound) The standard deviation of the sample meanis, S (Type an integradecimal Do not found) b. Determine the sampling abution of the sam e for samples 256 The mean of the sample means type an integer er domat Dentround) The standard deviation of the sample meani n g of a decimal Do not c. Do you need to assume that classroom teacher salaries are normal disbuted to answer purista) OA. Yes because is only normally distributed ti m ely disabled OB. Ne because it is normally distbuted the most be nomaly distributed OC. No, because the sample sizes are sufficiently large so that will be approximately normally distributed to the dirbution OD. Yes, because the sample sizes are not suficiently large so that will be approximately normally distributerades of the dibution of

Answer 1

(a)

For sample size 64

The mean of the sample mean is $\mu_{x}$ = $53.9 thousands

The standard deviation of the sample mean is $\sigma_{x}$ = $\frac{\sigma}{\sqrt{n}}$ = 8/√64

= $1.0 thousand = $1000

(b)

For sample size 256

The mean of the sample mean is $\mu_{x}$ = $53.9 thousands

The standard deviation of the sample mean is $\sigma_{x}$ = $\frac{\sigma}{\sqrt{n}}$ = 8/√256

= $0.5 thousand = $500

(c) No, because the sample sizes are sufficiently large so that $\bar{x}$ will be approximately normally distributed, regardless of the distribution of x

(d) Margin of error ≤ $1000

->

2*0, < 1000

-> z * $1000 ≤ 1000

-> z ≤ 1

The required probability = P(|z| ≤ 1)

= 0.683

(e) Margin of error ≤ $1000

-> z ≤ 1000/500

-> z ≤ 2

The required probability = P(|z| ≤ 2)

= 0.954