### Understanding the Sampling DistributionSuppose a simple random sample of size \( n = 75 \) is obtained from a population whose size is \( N = 10,000 \) and whose population proportion with a specified characteristic is \( p = 0.6 \). Complete parts (a) through (c) below.#### (a) Describe the Sampling Distribution of \( \hat{p} \)Choose the phrase that best describes the shape of the sampling distribution below:- **A.** Not normal because \( n \leq 0.05N \) and \( np(1 - p) \) < 10.- **B.** Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \).- **C.** Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \).- **D.** Not normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \).#### Determine the Mean of the Sampling Distribution of \( \hat{p} \)\[ \mu_{\hat{p}} = p \](Round to one decimal place as needed.)#### Determine the Standard Deviation of the Sampling Distribution of \( \hat{p} \)\[ \sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}} \](Round to six decimal places as needed.)#### (b) Probability for \( x \geq 48 \) Individuals with the CharacteristicWhat is the probability of obtaining \( x = 48 \) or more individuals with the characteristic? That is, what is \( P(\hat{p} \geq 0.64) \)?\[ P(\hat{p} \geq 0.64) = \] (Round to four decimal places as needed.)#### (c) Probability for \( x \leq 39 \) Individuals with the CharacteristicWhat is the probability of obtaining \( x = 39 \) or fewer individuals with the characteristic? That is, what is \( P(\hat{p} \leq 0.52) \)?\[ P(\hat{p} \leq 0.52) = \] (Round to four

Answered: Image /qna-images/answer/4d1fda6f-666d-4fd8-ae06-0774a37c4aa6.jpg

Answered: Suppose a simple random sample of size…

Suppose a simple random sample of size n= 75 is obtained from a popula specified characteristic is p = 0.6. Complete parts (a) through (c) below.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

7. Workers at a large toxic ceanup project are concerned that their white blood cell counts may have been reduced. Let x be a random variable that represents white blood cell count per cubic millimeter of whole blood in a healthy adult. Then u-7500 and a -1750 (Reference: Diagnostic Tests with Nursing Applications, S. Loeb). A random sample of n =50 workers from the toxic cleanup site were given a blood test that showed x = 6820. What is the probability that, for healthy adults, I will be this low or lower?
2. A population has member numbers 2, 4, 6, 8, 10, 12. Then 2 samples are taken at random and without replacement. If it is known that u =7 Find: - Population variance (o?) - The mean standard deviation of the sample (ox?)
2. City officials are interested in identifying the most dangerous intersections in State College. The city records the number of car accidents at each of n intersections over the course of the year. Let's assume that the number of accidents for a particular intersection i is denoted by X₁. We are provided with a simple random sample of accidents at n intersections, X₁,..., Xn. Let's assume the following model, i.i.d. Xi Pois (X) where A is an unknown parameter of interest (i.e., the unknown population accident rate). (a) the sufficient statistic? Show that the MLE of λ is X. Find its sufficient statistic. Is the MLE a function of Find the bias, variance, and MSE of ÂMLE. Does the MLE achieve the Cramér-Rao's lower bound? (b) (c) (d) Find the asymptotic distribution of the MLE for A. (e) Now, the officials are interested in the total number of accidents expected in those n intersections, that is, E(X1 X₂) = nλ. Let us denote this expected total as (= nλ). Find the MLE of 0. (Hint:…
OK 8.17 To emphasize safety, a taxicab company wants to estimate the proportion of unsafe tires on their 175 cabs (Ignore spare tires.) Selecting a simple random sample of tires is imprac- tical, so cluster sampling is used, with each cab as a cluster. A random sample of 25 cabs gives the following number of unsafe tires per cab: 2, 4, 0, 1, 2, 0, 4, 1, 3, 1, 2, 0, 1, 1, 2, 2, 4, 1, 0, 0, 3, 1, 2, 2, 1 Estimate the proportion of unsafe tires being used on the company's cabs and place a bound on the error of estimation.
15. The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 10.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eightfull-time faculty for one week is shown in the table below. At α=0.05, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 11.2 7.5 12.2 7.2 4.1 9.5 13.7 8.5 Question content area bottom Part 1 (a) Write the claim mathematically and identify H0 and Ha. Which of the following correctly states H0 and Ha? A. H0: μ>10.0 Ha: μ≤10.0 B. H0: μ≠10.0 Ha: μ=10.0 C. H0: μ<10.0 Ha: μ≥10.0 D. H0: μ≤10.0 Ha: μ>10.0 E. H0: μ≥10.0 Ha: μ<10.0
Suppose a simple random sample of size n = 200 is obtained from a population whose size is N=20,000 and whose population proportion with a specified characteristic is p=0.8. Complete parts (a) through (c) below. A. Approximately normal Decause ns. and per-p) 1. OB. Not normal because n ≤0.05N and np(1-p) 0.81)? P(p≥ 0.81)= 3632 (Round to four decimal places as needed.) (c) What is the probability of obtaining x= 150 or fewer individuals with the characteristic? That is, what is P(p ≤ 0.75)? P(p ≤ 0.75)= (Round to four decimal places as needed.) + example Get more help. alues % 5 A + 6 MacBook Pro & 7 * 00 8 Vi I, Clear all ( 9 More Check answer X
Only parts D and E please.
7)
7.29 only
a) Let X₁, X2, X3,..., X₁ be a random sample of size n from population X. Suppose that X follows an exponential distribution with parameter 0 and Y = ===1 X₁. n b) i) Show that y follows a chi-square distribution with 2n degrees of freedom. ii) What is the value of the sample size n, if P(Y > 20.4831) = 0.025? iii) What is the value of sample size n, if P(|Y - 2n| <40) ≥ 0.025? iv) Use the Central Limit Theorem to compute P(100 < Y < 115), for n = 40. Let X₁, X2, ..., X5 be a random sample of size 5 from the standard normally population. If the statistic Y is given by Y = X1 X2 X3 ₁²+X3² +X5² i) Briefly explain why Y follows a Student's t distribution with 3 degrees of freedom. ii) Compute the probability that Y is between 2.35 and 5.84. iii) What is the mean and variance of the statistic Y?
Consider the following population: {6, 7, 8, 9). For this population the mean is 6 + 7 + 8 + 9 4 μl = Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account). 6,7 8, 6 6,7 Sample Sample Mean 6,8 6,9 (a) Calculate the sample mean for each of the 12 possible samples. 7,6 = 7.5 7,8 7,9 6,8 6,9 7,6 8,7 8,9 8, 6 9,6 7,8 7,9 9, 79, 8