2. It is believed that the percent of female STEM majors at a particular college Is 29%.a) Say we select 15 random females from this college. Is this sample "large enough" touse the Central Limit Theorem for proportions? Use the conditions.b) Fill in the blank to write the sampling distribution when we obtain 100 females. Besure to check the assumptions. Round to three decimal points if possible.p~AN (

Given P-bar=0.29 For a) n=15 For b) n=100

Answered: 2. It is believed that the percent of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The Central Limit Theorem guarantees an approximately normal sampling distribution for the sample mean for samples having sizes less than or equal to 40, so no knowledge about the distribution of the population is necessary for the corresponding interval to be valid. a. True b. False
The central limit theorem states that as sample size increases, the sampling distribution of the mean becomes-- more normally distributed more normally distributed less normally distributed but more leptokurtic less normally distributed but more leptokurtic more shaped like the population distribution more shaped like the population distribution smaller than the population mean
Recall also that for large sample values, the Central Limit Theorem applies. That is, as the sample size n increases without limit, the shape of the distribution of the sample means taken from the population with mean μμ, and standard deviation σσ, will approach a normal distribution. So, with the application of the Central Limit Theorem, approximately 95% of the sample means taken from a population will fall within ±1.96±1.96standard errors of the population mean. Thus, the interval estimate is given by, μ−1.96(σn√)toμ+1.96(σN√)μ−1.96(σn)toμ+1.96(σN) The General Formula for confidence intervals for large samples is: lower confidence boundary or limit < population mean< upper confidence boundary or limit X−zα2(σn√)<μ<X+zα2(σn√)X−zα2(σn)<μ<X+zα2(σn) Also consider the following: Confidence Level zα2valueszα2values (confidence coefficients) 90% ±1.645±1.645 95% ±1.96±1.96 99% ±2.58±2.58 A Four-step Process in Computing the Interval Estimates Step…
The central limit theorem states that if all possible random samples of sizeNare drawnfrom a population with a mean ofμ ̄Xand a standard deviation ofσ ̄X, then asNbecomeslarger, the sampling distribution of sample means becomes approximately (_______) with a mean of (______) and a standard deviation of (______). Fill in the blanks
The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the National Council intends to estimate the proportion from a random sample. Let p be the proportion of small businesses that declared Chapter 11 bankruptcy last year. (a) If no preliminary sample is taken to estimate p, how large a sample is necessary to be 99% sure that a point estimate p̂ will be within a distance of 0.080 from p? (b) In a preliminary random sample of 30 small businesses, it was found that fourteen had declared Chapter 11 bankruptcy. How many more small businesses should then be included in a sample to be 99% sure that a point estimate p̂ will be within a distance of 0.080 from p?
What is the Central Limit Theorem? It is always true that as the sample size, n, increases, the distribution of the sample means will be approximately normally distributed. Explain
It is believed that the percent of female STEM majors at a particular college Is 29%. a)Say we select 15 random females from this college. Is this sample “large enough” to use the Central Limit Theorem for proportions? Use the conditions
It is known that 64% of Americans personally worry a great deal about federal spending and the budget deficit. Which of the following needs to be satisfied in order to be able to use the Central Limit Theorem to describe the sampling distribution of the proportion of Americans who personally worry a great deal about federal spending and the budget deficit? The sample needs to be representative of all Americans. If sampling without replacement, the sample size needs to be less than 5% of the population size. The sample size should not be less than 30. The expected numbers of those who do and do not personally worry a great deal about federal spending and the budget deficit need to both be at least 5.
4) The central limit theorem says as we increase the number of samplings n, the variance of the sampling distribution will __________.
There are about 11,000 births in the United States each day, and the proportion of boys is .512. If 100 births are randomly selected per day for 100 days, what is the probable mean of the sample proportion? b.) Name a provision for the Central Limit Theorem and the Sampling Distribution x-bar to be an accurate approximation for the population. c.) Name an alternative provision for the Central Limit Theorem and the Sampling Distribution x-bar to be an accurate approximation for the population.
The Central Limit Theorem is important in statistics because for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size. for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. for any sized sample, it says the sampling distribution of the sample mean is approximately normal. for a large n, it says the population is approximately normal.
3. The Central Limit Theorem states that the mean of the sampling distribution of the sample mean is A. larger than the population mean. B. exactly equal to the population mean. C. equal to the population mean divided by the square root of the sample size. D. close to the population means if the sample size is large.

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