CUET Mathematics Statistics & Applications > Inferential PYQs

(A), (B) and (D) only

(A), (B) and (C) only

(A), (B), (C) and (D)

(C) and (D) only

11

10

7

9

2.1

4.1

5.6

3.1

Strategy was effective as null hypothesis is accepted

Strategy was effective as null hypothesis is rejected

Strategy was not effective as null hypothesis is accepted

Strategy was not effective as null hypothesis is rejected

73

69

67

91.25

(321.06, 328.14)

(320.06, 327.14)

(322.06, 327.14)

(321.06, 327.14)

(A) and (C) only

(A) and (D) only

(B) and (C) only

(B) and (D) only

36

49

64

81

-3.79

-5.79

-4.79

-2.79

250, 150

150, 250

200, 200

200, 100

Mean

Variance

Standard Deviation

t-Statistic

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(A) - (IV), (B) - (III), (C) - (i), (D) - (II)

(A) - (III), (B) - (IV), (C) - (i), (D) - (II)

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

0.25

0.025

0.125

125

(A) - (IV), (B) - (II), (C) - (I), (D) - (III)

(A) - (I), (B) - (IV), (C) - (II), (D) - (III)

(A) - (III), (B) - (II), (C) - (IV), (D) - (I)

(A) - (I), (B) - (III), (C) - (II), (D) - (IV)

0.5

0.2

0.6

0.4

t (0.005)

t (0.01)

t (0.025)

t (0.05)

$\frac{n - m}{2}$

$\frac{n + m}{2}$

$n + m$

$n - m$

40

60

54

50

-1.8

-2.1

2.1

1.8

95

97

48

47

0.32

0.2

0.48

0.8

$\frac{3}{4}$

$\frac{1}{2}$

$\frac{3}{2}$

$\frac{5}{2}$

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(A) - (IV), (B) - (III), (C) - (I), (D) - (II)

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

(A), (B) and (C) only

(B), (C) and (D) only

(D) and (C) only

(C) and (D) only

3.612

3.126

3.162

3.216

5.32

2.67

34.26

5.71

(A) and (C) only

(B) and (C) only

(D) only

(A) and (B) only

(A) and (B) only

(B), (C) and (D) only

(A), (B), (C) and (D)

(A), (B) and (D) only

60

50

52

54

n

2n

n+1

n-1

9

10

11

12

1.03

1.33

1.43

1.53

Sample is a collection of some elements of population having same characteristic.

The measurable characteristic of sample is called statistic.

A survey done using a sample of the population has no margin of error.

The sample makes inference about the population.

1.93

2.84

1.54

1.64

15.21

10

3.898

3.192

(A), (B) and (D) only

(A), (B) and (C) only

(A), (B), (C) and (D)

(C) and (D) only

-1

-2

1

2

(A), (B) and (C) only

(A), (B) and (D) only

(A), (B), (C) and (D)

(C) and (D) only

Type-I error

Type-II error

Sampling error

Calculation error

120

81

96

112

(A), (B) and (D) only

(A), (B) and (C) only

(A), (B), (C) and (D)

(C) and (D) only

2.14

-1.54

0.84

1.988

1.5

4.9

3.1

9

(A), (B) and (D) only

(A) and (D) only

(A), (B), (C) and (D)

(B) and (C) only

(A), (B) and (D) only

(A), (C) and (D) only

(A) and (C) only

(C) and (D) only

$t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}} ; s = \sqrt{\frac{n_1s_1^2 + n_2s_2^2}{n_1 + n_2 - 2}}$

$t = \frac{\bar{x}_1 - \bar{x}_2}{s\sqrt{\frac{1}{n_1^2} + \frac{1}{n_2^2}}} ; s = \sqrt{\frac{n_1^2s_1^2 + n_2^2s_2^2}{n_1 + n_2 - 2}}$

$t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}} ; s = \sqrt{\frac{n_1s_1^2 + n_2s_2^2}{n_1 + n_2 - 2}}$

$t = \frac{\bar{x}_1 - \bar{x}_2}{s\sqrt{\frac{1}{n_1^2} + \frac{1}{n_2^2}}} ; s = \sqrt{\frac{n_1s_1^2 + n_2s_2^2}{n_1 + n_2 - 2}}$

A statistical hypothesis is a statement about the population parameter which may be true or false.

The standard deviation of the sampling distribution of a statistics is known as its standard error.

If sufficiently large random samples with replacement are drawn from a population, then the sampling distribution of the sample means approaches a binomial distribution.

In a statistical hypothesis testing, a Type-I error is made when null hypothesis is rejected when it is true.

2.5

1.5

2.36

0.512

The sampling distribution of the sample mean approaches a bell-shaped curve as the sample size gets larger.

A sample size of 30 or more is considered to be sufficient to hold the Central Limit Theorem.

As the sample size becomes larger, the prediction of characteristics of the population becomes more accurate.

The sampling distribution of the sample mean approaches a Poisson distribution as the sample size gets larger.

$n_1 + n_2 - 1$

$n_1 + n_2 - 2$

$n_1 + n_2 + 1$

$n_1 + n_2 + 2$

50

48

64

54

Population

Parameter

Population distribution

Statistic

1

4

9

25

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (IV), (B) - (III), (C) - (I), (D) - (II)

(A) - (I), (B) - (II), (C) - (IV), (D) - (III)

(A) - (IV), (B) - (I), (C) - (III), (D) - (II)

(A), (B) and (D) only

(A), (B) and (C) only

(B) and (D) only

(C) and (D) only

90

95

50

49

(A), (B), (C), (D)

(A), (C), (B), (D)

(B), (D), (A), (C)

(A), (B), (D), (C)

When the sample size increases, the mean of the sample of data becomes close to the mean of the overall population.

When the sample size increases, the sampling distribution of the mean approaches a normal distribution, regardless of the shape of the parent population.

A sample size of less than 30 is considered to be sufficient to hold the Central Limit Theorem.

A sample size of 30 or more is considered to be sufficient to hold the Central Limit Theorem.

$t = \frac{\bar{x}_1 - \bar{x}_2}{S_p\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$, where $S_p$ is pooled standard deviation.

$t = \frac{\bar{x}_1 - \bar{x}_2}{S_p\sqrt{\frac{1}{n_1} - \frac{1}{n_2}}}$, where $S_p$ is pooled standard deviation.

$t = \frac{\bar{x}_1 + \bar{x}_2}{S_p\sqrt{\frac{1}{n_1} - \frac{1}{n_2}}}$, where $S_p$ is pooled standard deviation.

$t = \frac{\bar{x}_1 + \bar{x}_2}{\sqrt{\frac{1}{n_1} - \frac{1}{n_2}}}$, where $S_p$ is pooled standard deviation.

Statistic

Sample

Parameter

Statistical Inference

(A), (B) and (C) only

(B), (C) and (D) only

(A), (C) and (D) only

(A) and (D) only

$12$

$30$

$21$

$24$

$96$

$125$

$54$

$81$