why CLT also works for sample proportion?
why CLT also works for sample proportion?
Homework Answers
When random variable X is continuous having distribution f(x) . Then sampling distribution of sample mean has has normal distribution if sample size is grater than 30.
In case of categorical variable, random variable X has binomial distribution. Since X is number of successes out of sample size n.
Then sample proportion holds CLT using mean and variance of binomial distribution of r.v. X.
CLT for proportions. Define the term “sampling distribution” of the sample proportion, and describe how the...
CLT for proportions. Define the term “sampling distribution” of the sample proportion, and describe how the shape, center, and spread of the sampling distribution change as the sample size increases when p = 0.1.
Why is the Central Limit Theorem useful? [Q8P5.3] a. Because when the conditions for the CLT...
Why is the Central Limit Theorem useful? [Q8P5.3] a. Because when the conditions for the CLT are met, it allows us to use a Normal distribution to approximate the distribution of the whole population, even if we don't know whether the population follows a Normal distribution. Because when the conditions of the CLT are met, it allows us to calculate the area in the tails of the population distribution and therefore the probability of obtaining an observation as or more...
Q5 (please also show the steps): CLT = Central Limit Theorem Q5 Consider a problem of estimating...
Q5 (please also show the steps):
CLT = Central Limit Theorem
Q5 Consider a problem of estimating the difference of proportions for two populations. In sample 1, out of n subjects, Si of them are "successes" and the rest are "failures". In sample 2, out of n2 subjects, S2 of them are "successes" and the rest are "failures". It is known that Si~ B(ni,P) and S2 ~ B(n2, p). We are interested in estimating P1 - P2. 1. Denote fi =...
Central Limit Theorem (CLT) 1. The CLT states: draw all possible samples of size _____________ from...
Central Limit Theorem (CLT) 1. The CLT states: draw all possible samples of size _____________ from a population. The result will be the sampling distribution of the means will approach the ___________________- as the sample size, n, increases. 2. The CLT tells us we can make probability statements about the mean using the normal distribution even though we know nothing about the ______________-
Discuss the differences between the sample proportion and the population proportion. Which is random and which...
Discuss the differences between the sample proportion and the population proportion. Which is random and which isn't? Why?
8. Using Minitab to illustrate the Central Limit Theorem (CLT), the CLT tells us about the...
8. Using Minitab to illustrate the Central Limit Theorem (CLT), the CLT tells us about the sampling distribution of the sample mean. With Minitab we can easily "sample" from a population with known properties (4,0 , shape). a. Our population consists of integer values X from 1 through 8, all equally likely P(x) = 1/8; x = 1, 2, 3, 4, 5, 6, 7, 8 o = 2.29 Using methods from the beginning of Chapter 4 in the textbook, find...
Which is a correct step in applying CLT? Highlight or circle one Collect a sample of...
Which is a correct step in applying CLT? Highlight or circle one Collect a sample of people, treating each person as one unit in the new distribution Collect a sample of people, treating the sample mean as one unit in the new distribution Make sure that the parent distribution is normal first, and then collect a sample of people, treating each person as one unit in the new distribution Make sure that the parent distribution has a standard deviation that...
Demonstrate Central Limit Theorem(CLT) of the sample mean by sampling a 100 uniform distribution data with 50 variables. Verify the result by computing the sample mean, sample variance and sketch the...
Demonstrate Central Limit Theorem(CLT) of the sample mean by sampling a 100 uniform distribution data with 50 variables. Verify the result by computing the sample mean, sample variance and sketch the histogram on Excel/Megastat. Hint: Generate 100 datasets of 50 variables and calculate 50 sample means to determine the distribution of X̅ and SX̅. It should converge to a model that we’ve learned in class.
PLEASE ANSWER CLEARLY Question Completion Status: One sample proportion summary confidence interval: P: Proportion of successes...
PLEASE ANSWER CLEARLY
Question Completion Status: One sample proportion summary confidence interval: P: Proportion of successes Method: Standard-Wald 95% confidence interval results: Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit р 68 285 0.23859649 0.025247422 0.18911245 0.28808053 a. Identify the 95% confidence interval for this given scenario. a. 18.9% < < 28.8% o b. 18.9% < < 28.8% 18.9% < X < 28.8% C 95% confidence interval results: Proportion Count Total Sample Prop. Std. Err. L. Limit...
In a population, 68% of all tax returns lead to a refund. A random sample of...
In a population, 68% of all tax returns lead to a refund. A random sample of 1000 tax returns is taken. (a) Describe the distribution of the number of returns leading to refunds in the sample. (b) What is the expected number of returns leading to refunds in the sample? What is its variance? (c) What is the mean of the sample proportion of returns leading to refunds? (d) What is the variance of the sample proportion? (e) What is...
Why is the Central Limit Theorem useful? [Q8P5.3] a. Because when the conditions for the CLT are met, it allows us to use a Normal distribution to approximate the distribution of the whole population, even if we don't know whether the population follows a Normal distribution. Because when the conditions of the CLT are met, it allows us to calculate the area in the tails of the population distribution and therefore the probability of obtaining an observation as or more...
Q5 (please also show the steps):
CLT = Central Limit Theorem
Q5 Consider a problem of estimating the difference of proportions for two populations. In sample 1, out of n subjects, Si of them are "successes" and the rest are "failures". In sample 2, out of n2 subjects, S2 of them are "successes" and the rest are "failures". It is known that Si~ B(ni,P) and S2 ~ B(n2, p). We are interested in estimating P1 - P2. 1. Denote fi =...
8. Using Minitab to illustrate the Central Limit Theorem (CLT), the CLT tells us about the sampling distribution of the sample mean. With Minitab we can easily "sample" from a population with known properties (4,0 , shape). a. Our population consists of integer values X from 1 through 8, all equally likely P(x) = 1/8; x = 1, 2, 3, 4, 5, 6, 7, 8 o = 2.29 Using methods from the beginning of Chapter 4 in the textbook, find...
PLEASE ANSWER CLEARLY
Question Completion Status: One sample proportion summary confidence interval: P: Proportion of successes Method: Standard-Wald 95% confidence interval results: Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit р 68 285 0.23859649 0.025247422 0.18911245 0.28808053 a. Identify the 95% confidence interval for this given scenario. a. 18.9% < < 28.8% o b. 18.9% < < 28.8% 18.9% < X < 28.8% C 95% confidence interval results: Proportion Count Total Sample Prop. Std. Err. L. Limit...
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