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

Question
Sampling distributions
asked 2021-02-20
Which of the following are correct general statements about the central limit theorem? Select all that apply
1. The accuracy of the approximation it provides, improves when the trial success proportion p is closer to \(50\%\)
2. It specifies the specific mean of the curve which approximates certain sampling distributions.
3. It is a special example of the particular type of theorems in mathematics, which are called Limit theorems.
4. It specifies the specific standard deviation of the curve which approximates certain sampling distributions.
5. It’s name is often abbreviated by the three capital letters CLT.
6. The accuracy of the approximation it provides, improves as the sample size n increases.
7. The word Central within its name, is mean to signify its role of central importance in the mathematics of probability and statistics.
8. It specifies the specific shape of the curve which approximates certain sampling distributions.

Answers (1)

2021-02-21
Step 1
Central Limit Theorem (CLT): - If \(X\sim N(\mu,\sigma)\) and sample size n are very large then the sample mean also follows a normal distribution.
Step 2
1) For the proportion, if np >10 and nq> 10 and the sample size is large then it follows the normal distribution. So, this is not correct.
2)CLT specifies the specific mean of the curve which approximates certain sampling distributions is true.
4) CLT specifies the specific standard deviation of the curve which approximates certain sampling distributions is correct.
5)Its name is often abbreviated by the three capital letters CLT is correct.
6)The accuracy of the approximation it provides, improves as the sample size n increases is correct.
8) CLT specifies the specific shape of the curve which approximates certain sampling distributions is correct.
0

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