**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 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
Assume the samples are random and independent, the populations are nomally distributed, and the population variances are equal. The table available below shows the prices (in dollars) for a sample of automobile batteries. The prices are classified according to battery type. At a = 0.10, is there enough evidence conclude that at least one mean battery price is different from the others? Complete parts (a) through (e) below. E Click the icon to view the battery cost data. (a) Let u1. P2. H3 represent the mean prices for the group size 35, 65, and 24/24F respectively. Identify the claim and state Ho and H. H Cost of batteries by type The claim is the V hypothesis. Group size 35 Group size 65 Group size 24/24F 101 111 121 124 D 146 173 182 278 124 140 141 89 (b) Find the critical value, Fo, and identify the rejection region. 90 79 84 The rejection region is F Fo, where Fo = (Round to two decimal places as needed.) (c) Find the test statistic F. Print Done F= (Round to two decimal places as…
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Which of the following is a characteristic of the sampling distribution of a mean or proportion? a) its standard error increases as the size of the sample increases b) its standard error increases as the size of the population increases c) it has the shape of a normal curve d) its shape depends on the shape of population distribution
According to a survey in a country, 32% of adults do not own a credit card. Suppose a simple random sample of 600 adults is obtained. Complete parts (a) through (d) 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, the sample proportion of adults who do not own a credit card. Choose the phrase that best describes the shape of the sampling distribution of p below. O A. Not normal because n <0.05N and np(1 – p)< 10 GB. Approximately normal because n<0.05N and np(1 - p) 2 10 CC. Not normal because ns0.05N and np(1 - p) 2 10 D. Approximately normal because n<0.05N and np(1 - p)< 10 Determine the mean of the sampling distribution of p. (Round to two decimal places as needed.) p Enter your answer in the answer box and then click Check Answer. ? 6. parts remaining Clear All Check Answer
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.)
4. You ask an SRS of 1500 college students whether they applied for admission to any other college. Suppose that in fact 35% of all college students applied to colleges besides the one they are attending. The sampling distribution of the proportion of B your sample who say "Yes" is approximately Normal with mean 0.35 and standard deviation 0.01. Sketch this Normal curve and use it to answer the following questions. (You can use the 68-95-99.7 rule for all these questions.) Round to nearest whole percent. (a) What percentage of many samples would have a larger than 0.37? 2.5 (b) What is the probability that your sample will have a less than 0.33?Å (c) what is the probability that your sample result will be either less than 0.33 or greater than 0.35?
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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…
The salaries of professional baseball players are heavily skewed right with a mean of $3.2 million and a standard deviation of $2 million. The salaries of professional football players are also heavily skewed right with a mean of $1.9 million and a standard deviation of $1.5 million. A random sample of 40 baseball players’ salaries and 35 football players’ salaries is selected. The mean salary is determined for both samples. Let represent the difference in the mean salaries for baseball and football players. Which of the following represents the shape of the sampling distribution for ? skewed right since the populations are both right skewed skewed right since the differences in salaries cannot be negative approximately Normal since both sample sizes are greater than 30 approximately Normal since the sum of the sample sizes is greater than 30
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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