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Yes. Roughly, very large samples are very likely to have subsets data points having very similar means and distributions. Large numbers of such subsets will tend to be normal distributed (Why?) and will tend to make the total sample be normally distributed.

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What is the sampling distribution when the standard deviation is known?

When the standard deviation of a population is known, the sampling distribution of the sample mean will be normally distributed, regardless of the shape of the population distribution, due to the Central Limit Theorem. The mean of this sampling distribution will be equal to the population mean, while the standard deviation (known as the standard error) will be the population standard deviation divided by the square root of the sample size. This allows for the construction of confidence intervals and hypothesis testing using z-scores.


What assumption will work best for a large data set with a normal distribution?

The assumption that works best for a large data set with a normal distribution is that the data follows a bell-shaped curve, characterized by symmetry around the mean. In this context, the Central Limit Theorem supports that as the sample size increases, the sampling distribution of the sample mean will also approach a normal distribution, regardless of the original data's distribution. This allows for the application of parametric statistical methods, such as t-tests or ANOVA, which rely on normality. Additionally, it is assumed that the data points are independent of each other.


Why you use z distribution?

A z distribution allows you to standardize different scales for comparison.


What allows you to enter calculate manipulate and analyze data such as numbers and text?

Worksheets allow users to enter, calculate, manipulate, and analyze data such as numbers and text. Worksheets means the same as spreadsheets.


What is the rule between free variation and the distribution of sound?

Free variation refers to instances where two or more sounds can occur in the same phonetic environment without altering the meaning of a word. In contrast, the distribution of sounds involves systematic patterns where certain sounds appear in specific contexts, often governed by phonological rules. While free variation allows for interchangeable sounds, distribution emphasizes the constraints and rules that determine when and where particular sounds can be used. Understanding both concepts helps linguists analyze phonetic and phonological behavior in languages.

Related Questions

Where is theorem used?

In circuits with multiple sources. This allows you to analyze the effects of each source separately, which often simplifies the math.


Why the normal distribution can be used as an approximation to the binomial distribution?

The central limit theorem basically states that for any distribution, the distribution of the sample means approaches a normal distribution as the sample size gets larger and larger. This allows us to use the normal distribution as an approximation to binomial, as long as the number of trials times the probability of success is greater than or equal to 5 and if you use the normal distribution as an approximation, you apply the continuity correction factor.


What is the sampling distribution when the standard deviation is known?

When the standard deviation of a population is known, the sampling distribution of the sample mean will be normally distributed, regardless of the shape of the population distribution, due to the Central Limit Theorem. The mean of this sampling distribution will be equal to the population mean, while the standard deviation (known as the standard error) will be the population standard deviation divided by the square root of the sample size. This allows for the construction of confidence intervals and hypothesis testing using z-scores.


What assumption will work best for a large data set with a normal distribution?

The assumption that works best for a large data set with a normal distribution is that the data follows a bell-shaped curve, characterized by symmetry around the mean. In this context, the Central Limit Theorem supports that as the sample size increases, the sampling distribution of the sample mean will also approach a normal distribution, regardless of the original data's distribution. This allows for the application of parametric statistical methods, such as t-tests or ANOVA, which rely on normality. Additionally, it is assumed that the data points are independent of each other.


What is the importance of work-energy theorem?

The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. This theorem is important because it allows us to analyze and predict the motion of objects by considering the work done on them. It provides a powerful tool for understanding and solving problems in mechanics.


What is the constent in the field of central force?

In the field of central force, the constant refers to the conservation of angular momentum of a particle moving under the influence of a central force. This constant allows us to analyze the motion of the particle and understand its behavior without explicitly solving the differential equations of motion.


Converse of Pythagorean Theorem?

The Pythagorean Theorem allows the mathematician to determine the value of the hypotenuse. The converse of the Pythagorean Theorem manipulates the formula so that the mathematician can use the values to determine that if the triangle is a right triangle.


Why you use z distribution?

A z distribution allows you to standardize different scales for comparison.


What network theorem is generally used in the analysis of vacuum tubes?

Thevenin's Theorem simplifies complex circuits into a single voltage source and series resistance. This allows analysis of load lines and operating points.


Describe how an osteoctyle located near a central canal can pass nutrients to osteocytes located far from the central canal?

The osteocyte near the central canal receives nutrients from blood vessels in the central canal. It can then pass these nutrients through gap junctions to neighboring osteocytes, which in turn pass them on to osteocytes located further away from the central canal. This process allows for the distribution of nutrients throughout the bone tissue.


What is a ticket booking system?

An airline's deckhouse that manages ticket distribution is called a Central Reservation System (CRS), or Computer Reservation System. It's responsible for storing and managing all flight-related information, inventory, and ticketing. ... It allows managers to control reservations on all distribution platforms.


What allows a user to plan track analyze events schedule?

Project Management Software