Statistics

Which theorem states that the larger the sample size, the closer the sample mean will be to the mean of the population?

• Central limit theorem

• Law of averages

• Law of large numbers.

• Chebyshev's inequality

Considering the set of observations, the percentage of values that lies within two standard deviations of the population mean is

• 68%

• 55%

• 95%

• 99.7%

The abbreviation of i.i.d stands for

• independent and identically distributed

• identically and independently distributed

• both

• none of these

In central limit theorem, the random variables are assumed to be

• independent

• identical

• with same means and same variances

• all the above

If X_n converges to 'a' in probability as the sample size increases, then which of these statements are true

(i) for any ε>0, P{|X_n-a|>ε}→1 as n→∞

(ii) for any ε>0, P{|X_n-a|<ε}→0 as n→∞

• (i) only

• (ii) only

• both (i) and (ii)

• neither (i) nor (ii)

The Central Limit Theorem says that the sampling distribution of the sample mean is approximately normal if

• all possible samples are selected

• the sample size is large

• the standard error of the sampling distribution is small

• the sample size is small

The Central Limit Theorem says that the mean of the sampling distribution of the sample means is

• equal to the population mean divided by the square root of the sample size

• close to the population mean if the sample size is large

• exactly equal to the population mean

• close to the population mean divided by the square root of the sample size

The Central Limit Theorem says that the standard deviation of the sampling distribution of the sample means is

• equal to the population standard deviation divided by the square root of the sample size

• close to the population standard deviation if the sample size is large

• exactly equal to the population standard deviation

• close to the population standard deviation divided by the square root of the sample size

Samples of size 25 are selected from a population with mean 40 and standard deviation 7.5. The mean of the sampling distribution of sample means is

• 7.5

• 8

• 40

• 25

Samples of size 25 are selected from a population with mean 40 and standard deviation 7.5. The standard error of the sampling distribution of sample means is

• 0.3

• 1.5

• 7.5

• 1.6