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- Multiple ChoicePlease save your changes before editing any questions.
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

- Multiple ChoicePlease save your changes before editing any questions.
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%

- Multiple ChoicePlease save your changes before editing any questions.
The abbreviation of i.i.d stands for

independent and identically distributed

identically and independently distributed

both

none of these

- Multiple ChoicePlease save your changes before editing any questions.
In central limit theorem, the random variables are assumed to be

independent

identical

with same means and same variances

all the above

- Multiple ChoicePlease save your changes before editing any questions.
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)

- Multiple ChoicePlease save your changes before editing any questions.
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

- Multiple ChoicePlease save your changes before editing any questions.
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

- Multiple ChoicePlease save your changes before editing any questions.
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

- Multiple ChoicePlease save your changes before editing any questions.
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

- Multiple ChoicePlease save your changes before editing any questions.
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