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# Central Limit Theorem

### Central Limit Theorem Explanation

Explain how the Central Limit Theorem can help you convince your boss that while you can't get rid of sampling error the results from your statistical work (that is based on sampling) can still be useful. HINT: This is more of a story response (i.e. discussion of theory) than a math response (i.e. numbers and calculations flying

### Importance of the Central Limit Theorem

Why is the Central Limit Theorem so important to the study of sampling distributions? A. It allows us to disregard the size of the sample selected when the population is not normal B. It allows us to disregard the shape of the sampling distributions when the size of the population is large C. It allows us to disregard

### Central Limit Theory

Population Parameters. A population consists of these values: 2,3,6,8,11,18 a) Find U (mu), mean; Find Sigma (std. deviation) b) List all the samples of size n= 2 that can be obtained without replacement c) Find the population of all values of x (with bar over it) by finding the mean of each sample from part (b) (d

### Central limit theorem question

State the Central Limit Theorem The time spent by a factory worker A packing a box is a random variable with mean 3.5 minutes and standard deviation 1 minute. The times spent packing any two boxes are independent. (i) What is the approximate probability that he packs 100 boxes in less than 6 hours? (ii) What is the appr

### Sampling Methods and Central Limit Theorem

The mean score of a college entrance test is 500, the standard deviation is 75 and the scores are normally distributed. a. What percent of the students scored below 320? b. What percent of the students scored between 400 and 525? c. Twenty percent of the students had a test score above what score?

### Sampling Methods and the Central Limit Theorem

A recent study by the Greater Los Angeles Taxi Drivers Association showed that the mean fare charged for service from Hermosa Beach to LA International Airport is \$18 and the standard deviation is \$3.50. We select a sample of 15 fares. a. What is the likelihood that the sample mean is between \$17 and \$20? b. What must you as

### Problem Set-up: Sampling Methods and the Central Limit Theorem

I need help setting this up: The area of study is Sampling Methods and the Central Limit Theorem. Consider the digits in the phone numbers on a randomly selected page of your local phone book a population. Make a frequency table of the final digit of 30 randomly selected phone numbers. For example, if a phone number is 55

### Prob Set-up: Sampling Methods and the Central Limit Theorem

The area of study is Sampling Methods and the Central Limit Theorem Consider all of the coins (pennies, nickels, quarters, etc.) in your pocket or purse as a population.Make a frequency table beginning with the current year and counting backward torecord the ages (in years) of the coins. For example, if the current year is 20

### Likelihood Tests

8.1.9 Let X1,X2...,Xn be iid with pfm f(x;p)=p^x*(1-p)^(1-x), x=0,1, zero elsewhere. C={(x1,...,xn): Sum from 1 to n xi <=c} is the best critical region for testing H0: p=1/2 against p=1/3. Use the Central Limit Theorem to find n and c so that approximately P(Sum from 1 to n Xi <=c; H0) = 0.10 and P(sum from 1 to n Xi<=c; H1)=

### Maximum Likelihood Tests

Let X1,X2...,Xn be a random sample from a Bernoulli b(1, theta) distribution, where 0<theta<1. For n=100 and theta(0)=1/2, find c1 so that the test rejects H0 when Y<= c1 or Y>= 100-c1 has the approximate significance level of alpha=0.05. Hint: Use the Central Limit Theorem.

### Random Variable (Chebyshev's inequality; Central Limit Theorem)

If X is a Gamma random variable with parameters (n,1), approximately how large need n be so that ....... Answer: (a) Using Chebyshev's inequality; (b) the Central Limit Theorem

### Probability regarding a sample mean (central limit theorem)

Question: Men have hips normally dist. with a mean of 14.4 in. & s.d. of 1.0. Assume 2 male riders randomly selected. Find the probability that their mean hip width is greater than 15.5 in. Please show steps to arrive at the solution Also: Is the design appropriate assuming that the 2 men have a mean breadth of 16.75 inch

### Normal distribution probability - Central Limit Theorem

Assume men's weights are normally distributed w/ a mean of 172 lb. and a s.d. of 29lb. (a) If one man randomly selected, find the probability his weight is between 166 and 176 lb. ( b) If 16 men selected, find the probability that the mean weight is between 166 and 176 lb.

### Probability distribution of a sample mean

A wholesaler assures retailer replacement times for TVs normally dist. with mean of 8.2 and s.d. of 1.1. The retailer finds that a random sample of 20 sets from the wholesaler have mean replacement time of 7.6 years. Find P of getting a sample of 20 TVs with a mean replacement time of 7.6 years or less. Is wholesaler trustwort

### Assume men's weights are normally distributed...

Assume men's weights are normally distributed with a mean of 172 lb and an s.d. of 29lb. If one selected find P his weight is between 163 and 176lb. Part B is my problem-using the central limit theorem, if 16 men are randomly selected, find the P they have a mean weight between 166lb and 176 lb. The answer is not .5118 bu

### Sample Mean Probabilities with the Central Limit Theorem

Survey of 1976-80 found that the mean serum cholesterol level for U.S. males aged 20-74 years was 211. The standard deviation was approximately 90. Consider the sampling distribution of the sample mean based on samples of size 100 drawn from this population of males. 1. What are the mean of the sampling distribution? 2. Wh

### Mean Weight Randomly Selected

U= 143 lb, Stand. Dev. = 29 lb. 1a) If one woman is randomly selected, find the P that her weight is above 140 lb. I get 5517-what now??? 1b) If 100 women are selected randomly, find the P that they have a mean weight greater than 140lb. (Central limit theorem)

### Central Limit Theorem

U=143lb, Standard Deviant = 29 lb a) If 1 woman is randomly selected, find the probability that her weight is above 140 b) If 100 women are randomly selected, find the probability that they have a mean of over 140 lb. I believe the theroem is used only on part b.

### This problem uses the central limit theorem and a single sample hypothesis test to make an inference about a population mean. The decision rule for the test uses the p-value method.

A medical research study showed that the average weight of a newborn twin in 1988 was 5.1 lb. To determine if this year's average exceeds the 1988 mean of 5.1 lb., we would test the hypothesis; Ho (null hypothesis): mu = 5.1 lb. Ha (alternative hypothesis): mu > 5.1 lb. Where mu is the actual mean

### Central Limit Theorem and single sample hypothesis test,,.

A spokesman for a popular television game show claims that contestants on the show win an average of \$1200. In a random sample, 35 contestants were questioned on the amount of money they had won in order to test the hypothesis. The null hypothesis or Ho: the population mean equals \$1200, The alternative Hypothes

### Central limit theorem/sampling distribution of a sample mean

A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 milliliters. In fact, the contents vary according to a normal distribution with mean=298 ml and standard deviation=3 ml. a)What is the probability that an individual bottle contains less than 295 ml? b)What is t

### Central limit theorem/Sampling distribution of a sample mean

An SRS of 400 American adults is asked, "What do you think is the most serious problem facing out schools?" Suppose that in fact 30% of all adults would answer "drugs" if asked this question. The proportion X of the sample who answers "drugs" will vary in repeated sampling. In fact, we can assign probabilities to values of X us