Measures of Dispersion Test

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Measures of Dispersion Test - 23

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Question 1
1 / -0

The standard error of two means is equal to__________.

A
$$\sqrt{\dfrac{{\sigma}^{2}_{1}}{{n}_{1}}+\dfrac{{\sigma}^{2}_{2}}{{n}^2}}$$

B
$$\dfrac{\sigma}{\sqrt{n-1}}$$

C
$$\dfrac{\sigma}{\sqrt{n+1}}$$

D
$$\sqrt{\dfrac{{P}_{1}{Q}_{1}}{\sqrt{n}_{1}}+\dfrac{{P}_{2}{Q}_{2}}{{n}_2}}$$

Solution

The difference between the mean of two samples drawn randomly from the same source of population refers to the standard error of two means and the formula for calculation is given above.
Question 2
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The value of $$X^2$$ describes the magnitude of the difference between___________.

A
two normal distributions

B
expected and observed frequency

C
both (A) and (B)

D
two samples

Solution

Chi square distribution is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis.
Question 3
1 / -0

Standard error measures the dispersion from the_________-.

A
arithmetic mean

B
geometric mean

C
both (A) and (B)

D
harmonic mean

Solution

Standard error is a statistical term that measures the accuracy with which sample represents the population. It measures the dispersion of sample arithmetic mean from the population mean.
Question 4
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Which of the following are true or false?
a) T-distribution varies from+infinity to-infinity.
b)The variance of t distribution and the variance of normal distribution become closer and closer as the size of the sample increases.

A
both (a) and (b) are true

B
both (a) and (b) are false

C
(a) is true but (b) is false

D
(a) is false but (b) is true

Solution

Both (a) and (b) statements regarding students t-distribution is correct i.e. its value varies from +infinity to-infinity and the variance of t distribution and the variance of normal distribution become closer and closer as the sample size increases and also the variance of t distribution is always greater than 1.
Question 5
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If the standard deviation is small, we define a new variable known as ________.

A
student's F-distribution

B
student's T-variable

C
chi-square distribution

D
student's G-variable

Solution

If the standard deviation is small, it signifies that data are closely distributed around the mean value instead of widely spread and here, we define a new variable as Students T-variable.
Question 6
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The question of accepting or rejecting a hypothesis drawn depends upon ___________.

A
the information supplied by the sample data

B
the information supplied by the standard deviation

C
both (A) and (B)

D
none of the above

Solution

In hypothetical testing, data set obtained by sampling is compared to a synthetic data set from an idealised model.So the question of accepting or rejecting a hypothesis depends upon the information supplied by sample data.
Question 7
1 / -0

T-distribution is symmetrical like normal distribution and its mean value is____________.

A
zero

B
-1

C
1

D
2

Solution

The mean of t distribution is always equal to 0 and also the variance is always greater than 1 and it is symmetrical like normal distribution.
Question 8
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A simple formula to calculate the standard error is___________.

A
$$S_{yx} =$$ $${\sigma}_{y}{\sqrt{1 - {r}^2}}$$

B
$$S_{xy} =$$ $${\sigma}_{x}{\sqrt{1 - {r}^2}}$$

C
$$S_{yx} = $$ S.E.

D
Both (A) and (B)

Solution

Standard error can be calculated by applying two formulas mentioned in option A and option B that shows how a sample mean deviates from the mean of whole population.
Question 9
1 / -0

For a large sample, the sampling distribution of $$X^2$$ may form________.

A
a continuous curve

B
severely skewed curve

C
the symmetrical curve

D
either (B) or (C)

Solution

For a large sample, the sampling distribution of Chi square distribution may form a continuous curve. Chi square distribution helps in measuring how well the observed distribution of data fits with the distribution that is expected.
Question 10
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Which of the following is not true?

A
Standard Deviation is the most widely used measure of dispersion

B
Standard Deviation is not based on all values

C
A change in even one value affects the value of standard deviation

D
It is independent of origin but not of scale.

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Measures of Dispersion Test - 23

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Measures of Dispersion Test - 23

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SHARING IS CARING

Question 1

$$\sqrt{\dfrac{{\sigma}^{2}_{1}}{{n}_{1}}+\dfrac{{\sigma}^{2}_{2}}{{n}^2}}$$

$$\dfrac{\sigma}{\sqrt{n-1}}$$

$$\dfrac{\sigma}{\sqrt{n+1}}$$

$$\sqrt{\dfrac{{P}_{1}{Q}_{1}}{\sqrt{n}_{1}}+\dfrac{{P}_{2}{Q}_{2}}{{n}_2}}$$

Solution

Question 2

two normal distributions

expected and observed frequency

both (A) and (B)

two samples

Solution

Question 3

arithmetic mean

geometric mean

both (A) and (B)

harmonic mean

Solution

Question 4

both (a) and (b) are true

both (a) and (b) are false

(a) is true but (b) is false

(a) is false but (b) is true

Solution

Question 5

student's F-distribution

student's T-variable

chi-square distribution

student's G-variable

Solution

Question 6

the information supplied by the sample data

the information supplied by the standard deviation

both (A) and (B)

none of the above

Solution

Question 7

zero

-1

1

2

Solution

Question 8

$$S_{yx} =$$ $${\sigma}_{y}{\sqrt{1 - {r}^2}}$$

$$S_{xy} =$$ $${\sigma}_{x}{\sqrt{1 - {r}^2}}$$

$$S_{yx} = $$ S.E.

Both (A) and (B)

Solution

Question 9

a continuous curve

severely skewed curve

the symmetrical curve

either (B) or (C)

Solution

Question 10

Standard Deviation is the most widely used measure of dispersion

Standard Deviation is not based on all values

A change in even one value affects the value of standard deviation

It is independent of origin but not of scale.

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