**Understanding Sampling Distributions**In this exercise, we examine a simple random sample of size \( n = 75 \) taken from a population with size \( N = 10,000 \) and a specified population proportion \( p = 0.4 \).**Step 1: Describe the Sampling Distribution of \( \hat{p} \).**- To understand the shape of the sampling distribution, choose the appropriate description below: - **A. Not normal because \( n \leq 0.05N \) and \( np(1-p) \geq 10 \).** - **B. Approximately normal because \( n \leq 0.05N \) and \( np(1-p) \geq 10 \).** ✔️ - **C. Not normal because \( n \leq 0.05N \) and \( np(1-p) < 10 \).** - **D. Approximately normal because \( n \leq 0.05N \) and \( np(1-p) < 10 \).****Step 2: Determine the Mean of the Sampling Distribution of \( \hat{p} \).**- The mean of the sampling distribution \( \mu_{\hat{p}} = p \).- Enter the mean, rounded to one decimal place as needed.**Resources:**- For further assistance, options include "Help me solve this," "View an example," or "Get more help."This task involves basic statistical principles to understand how sample proportions relate to the population proportion through a normal distribution under specific conditions.

Answered: Image /qna-images/answer/e4c2dc49-5e47-4920-846d-7e3c58ba4414.jpg

Answered: Suppose a simple random sample of size…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that the efficacy of a certain drug is 0.47. Consider the sampling distribution (sample size n= 179) for the proportion of patients cured by this drug.What is the mean of this distribution? What is the standard error of this distribution? Round your answer to two decimal places.
Suppose the true proportion of voters in the county who support a specific candidate is 0.48. Consider the sampling distribution for the proportion of supporters with sample size n = 177. What is the mean of this distribution? What is the standard error (i.e. the standard deviation) of this sampling distribution, rounded to three decimal places?
Suppose a simple random sample of size n = 200 is obtained from a population whose size is N = 15,000 and whose population proportion with a specified characteristic is p = 0.2. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. O A. Not normal because n ≤0.05N and np(1-p) 10. O D. Approximately normal because n ≤0.05N and np(1-p) < 10. Determine the mean of the sampling distribution of p. (Round to one decimal place as needed.) Hp C
There are 120 students at Francis Howell North High School. Mr. Willott conducts a poll that asks 20 randomly selected students how many hours of sleep they got last night. They find that the mean amount of sleep is 6.7 hours. The population standard deviation is o = 2 hours. Can we estimate the standard deviation of the sampling distribution of means by using %3D V20 0.447 hours? O No, because we don't know that the distribution of sleep hours for the population is approximately Nor. O No, because we can't be sure that the central limit theorem applies to this situation. O Yes, because all the conditions for using this formula have been met. O No, because "hours of sleep" is not a continuous variable. O No, because the sample is more than 10% of the population.
Suppose a sample of O-rings was obtained and the wall thickness (in inches) of each was recorded. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed.. Click here to view the table of critical values for normal probability plots Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. 0.180 0.188 0.192 0.199 0.213 0.218 0.227 0.240 0.264 0.266 0.287 0.288 0.303 0.304 0.317 0.308 Using the correlation coefficient of the normal probability plot, is it reasonable to conclude that the population is normally distributed? Select the correct choice below and fill in the answer boxes within your choice. (Round to three decimal places as needed.) OA. Yes. The correlation between the expected z-scores and the observed data, data come from a normal population. OB. No. The correlation between the expected z-scores and the observed data, that…
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Suppose a simple random sample of size n= 50 is obtained from a population whose size is N= 10,000 and whose population proportion with a specified characteristic is p= 0.4. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. YA. Approximately normal because ns0.05N and np(1- p) 2 10. O B. Approximately normal because ns0.05N and np(1- p) < 10. O C. Not normal because ns 0.05N and np(1 - p) 2 10. O D. Not normal because ns0.05N and np(1- p) < 10. Determine the mean of the sampling distribution of p. HA = (Round to one decimal place as needed.)
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Suppose a simple random sample of size n = 1000 is obtained from a population whose size is N= 2,000,000 and whose population proportion with a specified characteristic is p = 0.61. Complete parts (a) through (c) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) Describe the sampling distribution of p. O A. Approximately normal, uA = 0.61 and aa z 0.0003 O B. Approximately normal, ua = 0.61 and aa 0.0002 OC. Approximately normal, ua = 0.61 and aa 0.0154 O Standard Normal Distribution Table (page 2) Aca Standard Normal Distribution 0.00 0.01 0,02 0.03 0.04 0.05 0,06 0,07 0.08 0.09 0.5000 0.5398 0.5793 0.6179 0.6554 0.5040 0.5438 0.5832 0.5080 0.5478 0.5871 0.6255 0.6628 0.5120 0.5517 0.5910 0.6293 0.6664 0.5160 0.5557 0.5948 0.6331 0.6700 0.5199 0.5596 0.5987 0.5239 0.5636 0.6026 0.6406 0.6772 0.5279 0.5675 0.6064 0.6443 0.6808 0.5319 0.5714 0.6103 0.6480 0.6844 0.5359 0.5753 0.6141 0.6517…
If the sample size is large, the normal distribution could be used for the interval estimate of the population proportion pTrue or False

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