Question

Which of the following are correct general statements about the Central Limit Theorem? Select all that apply. 1. It specifies the specific shape of th

Sampling distributions
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asked 2020-12-25

Which of the following are correct general statements about the Central Limit Theorem? Select all that apply.
1. It specifies the specific shape of the curve which approximates certain sampling distributions.
2. It’s name is often abbreviated by the three capital letters CLT
3. The word Central within its name, is meant to signify its role of central importance in the mathematics of probability and statistics.
4. The accuracy of the approximation it provides, improves when the trial success proportion p is closer to \(50\%\).
5. It specifies the specific mean of the curve which approximates certain sampling distributions.
6. The accuracy of the approximation it provides, improves as the sample size n increases.
7. It specifies the specific standard deviation of the curve which approximates certain sampling distributions.
8. It is a special example of the particular type of theorems in mathematics, which are called limit theorems.

Answers (1)

2020-12-26

Step 1
-The distribution of means is defined as the distribution of all possible sample means for a sample of a provided size.
-If a variable follows the normal distribution, then the mean \(\overline{x}\).
-follows the normal distribution, regardless of the sample size.
-The theorem states that the sampling distribution of sample means follows normal distribution for large sample size, i.e, greater than 30.
-The mean of the sampling distribution of sample means is \(\mu\).
=The standard deviation of the sampling distribution of sample mean is Statistics homework question answer, \(\sigma/\sqrt{n}\)
Therefore, if the sample size is greater than 30, the central limit theorem can be applied.
Step 2
The correct general statements about the Central Limit Theorem is:
1. It specifies the specific shape of the curve which approximates certain sampling distributions.
2. It’s name is often abbreviated by the three capital letters CLT.
3. It specifies the specific mean of the curve which approximates certain sampling distributions.
4. The accuracy of the approximation it provides, improves as the sample size n increases.
5. It specifies the specific standard deviation of the curve which approximates certain sampling distributions.

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