A simple random sample of size n = 36 is obtained from a population that is skewed left with μ = 86 and σ = 2. Does the population need to be normally distributed for the sampling distribution of x̄ to be approximately normally distributed? Why? What is the sampling distribution of x̄? --- **Does the population need to be normally distributed for the sampling distribution of x̄ to be approximately normally distributed? Why?** - **A.** ✔️ No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of x̄ becomes approximately normal as the sample size, n, increases. - **B.** No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x̄ become approximately normal as the sample size, n, increases. - **C.** Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x̄ normal, regardless of the sample size, n. - **D.** Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. **What is the sampling distribution of x̄? Select the correct choice below and fill in the answer boxes within your choice. (Type integers or decimals rounded to three decimal places as needed.)** - **A.** The shape of the sampling distribution of x̄ is unknown with μx̄ = [ ] and σx̄ = [ ]. - **B.** The sampling distribution of x̄ is uniform with μx̄ = [ ] and σx̄ = [ ]. - **C.** The sampling distribution of x̄ is skewed left with μx̄ = [ ] and σx̄ = [ ]. - **D.** The sampling distribution of x̄ is approximately normal with μx̄ = [ ] and σx̄ = [ ].

Consider random samples of size 258 drawn from population A with proportion 0.17 and random samples of size 310 drawn from population B with proportion 0.27. (a) Find the standard error of the distribution of differences in sample proportions, P - PB- Round your answer for the standard error to three decimal places. standard error = (b) Are the sample sizes large enough for the Central Limit Theorem to apply? OYes O No

tion list estion 11 estion 12 estion 13 estion 14 estion 15 estion 16 estion 17 crunch A simple random sample of size n = 53 is obtained from a population that is skewed left with μ=77 and o=4. Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? the sample size increases. OB. Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size, n. OC. No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x become approximately normal as the sample size, n, increases. OD. No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of x becomes approximately normal as the sample size, n, increases. What is the…

4. The pmf of a geometric distribution with parameter p is given by S p(1 – p)" n= 0, 1, 2, ... otherwise. Pn = Assume p> 0. Show that the variance is (1 – p)/p². Hint: Σ Eng" (1 – q)² n=0 for |g| < 1.

G A simple random sample of size n=36 is obtained from a population that is skewed left with p=86 and o=2. Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? Save Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? A. No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of x becomes approximately normal as the sample size, n, increases. B. No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x become approximately normal as the sample size, n, increases. O C. Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample…

Question 14 The Central Limit Theorem states that the sampling distribution of a sample mean, y, is approximately normal for O a. random samples taken from populations not known to be Normal if the sample size is large enough O b. The Central Limit Theorem states that the sampling distribution of the sample mean can never be approximated by a Normal Model O c. only random samples taken from populations that follow a Normal Model O d. small, biased samples taken from skewed populations A Moving to another question will save this response. etv 20 F9 임□ F3 F5 esc F2 F4 F1 # $ & * @ 5 8. 2 3 Q W E R tab A S D F H caps lock

Q.4-52

(b) Compute an 88.9% Chebyshev interval around the population mean. Recall that Chebyshev's Theorem states that for any set of data and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least 1 - Therefore, for data with mean u and standard deviation a, at least 1 - of data must fall between u- ko and + ko. When k- 3, we have the following. 1- 1 or 88.9% Therefore, for any set of data, at least 88.9% of the data must fall between - 3a and or, in other words, within standard deviations of the mean.

A random sample of size 10 yielded roughly "mound-shaped" data with a sample mean of 63.5 and a sample variance of 60.8. Let (L, OU) be the interval estimate that contains the population mean with 95% probability. Find the width of the interval. That is, find 0 – 0₁. 4.52 5.49 5.58 5.70 9.04 10.99 11.16 11.40 none of the other answers give the correct width