Question

Which of the following is NOT a conclusion of the Central Limit Theorem? Choose the correct answer below. a) The distribution of the sample means x ov

Limits and continuity
ANSWERED
asked 2021-06-07
Which of the following is NOT a conclusion of the Central Limit​ Theorem? Choose the correct answer below.
a) The distribution of the sample means x over bar x ​will, as the sample size​ increases, approach a normal distribution.
b) The distribution of the sample data will approach a normal distribution as the sample size increases.
c) The standard deviation of all sample means is the population standard deviation divided by the square root of the sample size.
d) The mean of all sample means is the population mean \(\mu\)

Answers (1)

2021-06-08
Step 1
The incorrect options are identified below
If the sample size increases, then the distribution of the sample mean leads to normal distribution. The standard deviation of all sample means is the ratio of the population standard deviation to the square root of sample size, moreover the expected value of all sample means is equal to the population mean.
When the sample size sufficiently large then the distribution of sample mean leads to normal and the expected value of all sample means equal to population mean. The standard deviation of all sample means is equal to the population standard deviation divided by the square root of sample size.
Step 2
The correct option is identified below:
When sample size increases the distribution of sample data will not follow normal distribution but the average of sample mean leads normal.
The distribution of the sample data will approach a normal distribution as the sample size increases is not a conclusion of central limit theorem.
According to central limit theorem the distribution of sample data does not follow normal distribution as the sample size increases or decreases but the average of sample mean follows normal distribution.
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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.
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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.
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