12th Business Maths Monthly Test - 2 ( Sampling techniques and Statistical Inference )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Monthly Test - 2 ( Sampling techniques and Statistical Inference )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

___________ is a relative property, which states that one estimator is efficient relative to another.

efficiency
sufficiency
unbiased
consistency

An estimate of a population parameter given by two numbers between which the parameter would be expected to lie is called an ___________ nterval estimate of the parameter.

point estimate
interval estimation
standard error
confidence

Errors in sampling are of

Two types
three types
four types
five types

Type II error is

Accept H₀ when it is wrong
Accept H₀ when it is true
Reject H₀ when it is true
Reject H₀ when it is false

An estimator is a sample statistic used to estimate a

population parameter
biased estimate
sample size
census

In ___________ the heterogeneous groups are divided into homogeneous groups.

Non-probability sample
a simple random sample
a stratified random sample
systematic random sample

If probability \(P[|\breve { \theta } -\theta |<\varepsilon ]\rightarrow 1\mu \quad as\quad n\rightarrow \infty ',\) for any positive \(\varepsilon \) then \(\breve { \theta } \) is said to _____________ esitimator of \(\theta\).

efficient
sufficient
unbiased
consistent

Type I error is

Accept H₀ when it is true
Accept H₀ when it is false
Reject H₀ when it is true
Reject H₀ when it is false.

In simple random sampling from a population of units, the probability of drawing any unit at the first draw is

\(\frac{n}{N}\)
\(\frac{1}{N}\)
\(\frac{N}{n}\)
1

A_________is one where each item in the universe has an equal chance of known opportunity of being selected.

Parameter
random sample
statistic
entire data

A __________ of statistical individuals in a population is called a sample.

Infinite set
finite subset
finite set
entire set

A random sample is a sample selected in such a way that every item in the population has an equal chance of being included

Harper
Fisher
Karl Pearson
Dr. Yates

Which one of the following is probability sampling

purposive sampling
judgment sampling
simple random sampling
Convenience sampling

A …………. may be finite or infinite according as the number of observations or items in it is finite or infinite.

Population
census
parameter
none of these

The method of obtaining the most likely value of the population parameter using statistic is called _____________

estimation
estimator
biased estimate
standard error.

Part - B

Generic 2 - Answer All Question

What is confidence interval?
In a sample of 400 population from a village 230 are found to be eaters of vegetarian items and the rest non-vegetarian items. Compute the standard error assuming that both vegetarian and non-vegetarian foods are equally popular in that village?

Explain in detail about the test of significance for single mean

The mean breaking strength of cables supplied by a manufacturer is 1,800 with a standard deviation 100. By a new technique in the manufacturing process it is claimed that the breaking strength of the cables has increased. In order to test this claim a sample of 50 cables is tested. It is found that the mean breaking strength is 1,850. Can you support the claim at 0.01 level of significance.

Explain the types of sampling.

Explain in detail about systematic random sampling with example.

The average score on a nationally administered aptitude test was 76 and the corresponding standard deviation was 8. In order to evaluate a state’s education system, the scores of 100 of the state’s students were randomly selected. These students had an average score of 72. Test at a significance level of 0.05 if there is a significant difference between the state scores and the national scores.

Explain the procedures of testing of hypothesis

Part - C

Generic 3 - Answer All Question

Using the following random number table,

Tippet’s random number table

2952 6641 3992 9792 7969 5911 3170 5624

4167 9524 1545 1396 7203 5356 1300 2693

2670 7483 3408 2762 3563 1089 6913 7991

0560 5246 1112 6107 6008 8125 4233 8776

2754 9143 1405 9025 7002 6111 8816 6446

Draw a sample of 10 children with theirheight from the population of 8,585 children as classified hereunder.

Height (cm) 105 107 109 111 113 115 117 119 121 123 125

Number of children 2 4 14 41 83 169 394 669 990 1223 1329

Height(cm) 127 129 131 133 135 137 139 141 143 145

No. of children 1230 1063 646 392 202 79 32 16 5 2

A sample of 100 students is chosen from a large group of students. The average height of these students is 162 cm and standard deviation (S.D) is 8 cm. Obtain the standard error for the average height of large group of students of 160 cm?

From the following data, select 68 random samples from the populationof heterogeneous group with size of 500 through stratified random sampling, considering the following categories as strata.
Category1: Lower income class -39%
Category2: Middle income class - 38%
Category3: Upper income class- 23%
Find the sample size for the given standard deviation 10 and the standard error with respect of sample mean is 3.

A server channel monitored for an hour was found to have an estimated mean of 20 transactions transmitted per minute. The variance is known to be 4. Find the standard error.

Using the Kendall-Babington Smith - Random number table,Draw5 random samples.

23 15 75 48 59 01 83 72 59 93 76 24 97 08 86 95 23 03 67 44

05 54 55 50 43 10 53 74 35 08 90 61 18 37 44 10 96 22 13 43

14 87 16 03 50 32 40 43 62 23 50 05 10 03 22 11 54 36 08 34

38 97 67 49 51 94 05 17 58 53 78 80 59 01 94 32 42 87 16 95

97 31 26 17 18 99 75 53 08 70 94 25 12 58 41 54 88 21 05 13

The standard deviation of a sample of size 50 is 6.3. Determine the standard error whose population standard deviation is 6?

Using the following random number table (Kendall-Babington Smith)

23 15 75 48 59 01 83 72 59 93 76 24 97 08 86 95 23 03 67 44

05 54 55 50 43 10 53 74 35 08 90 61 18 37 44 10 96 22 13 43

14 87 16 03 50 32 40 43 62 23 50 05 10 03 22 11 54 36 08 34

38 97 67 49 51 94 05 17 58 53 78 80 59 01 94 32 42 87 16 95

97 31 26 17 18 99 75 53 08 70 94 25 12 58 41 54 88 21 05 13

Draw a random sample of 10 four- figure numbers startingfrom 1550 to 8000.

Part - D

Generic 5 - Answer All Question

(i) A sample of 900 members has a mean 3.4 cm and SD 2.61 cm. Is the sample taken from a large population with mean 3.25 cm. and SD 2.62 cm?
(ii) If the population is normal and its mean is unknown, find the 95% and 98% confidence limits of true mean.

The mean life time of a sample of 169 light bulbs manufactured by a company is found to be 1350 hours with a standard deviation of 100 hours. Establish 90% confidence limits within which the mean life time of light bulbs is expected to lie.

A machine produces a component of a product with a standard deviation of 1.6 cm in length. A random sample of 64 componentsvwas selected from the output and this sample has a mean length of 90 cm. The customer will reject the part if it is either less than 88 cm or more than 92 cm. Does the 95% confidence interval for the true mean length of all the components produced ensure acceptance by the customer?

A manufacturer of ball pens claims that a certain pen he manufactures has a mean writing life of 400 pages with a standard deviation of 20 pages. A purchasing agent selects a sample of 100 pens and puts them for test. The mean writing life for the sample was 390 pages. Should the purchasing agent reject the manufactures claim at 1% level?

The mean weekly sales of soap bars in departmental stores were 146.3 bars per store. After an advertising campaign the mean weekly sales in 400 stores for a typical week increased to 153.7 and showed a standard deviation of 17.2. Was the advertising campaign successful?
An auto company decided to introduce a new six cylinder car whose mean petrol consumption is claimed to be lower than that of the existing auto engine. It was found that the mean petrol consumption for the 50 cars was 10 km per litre with a standard deviation of 3.5 km per litre. Test at 5% level of significance, whether the claim of the new car petrol consumption is 9.5 km per litre on the average is acceptable.

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Tippet’s random number table
2952	6641	3992	9792	7969	5911	3170	5624
4167	9524	1545	1396	7203	5356	1300	2693
2670	7483	3408	2762	3563	1089	6913	7991
0560	5246	1112	6107	6008	8125	4233	8776
2754	9143	1405	9025	7002	6111	8816	6446

Height (cm)	105	107	109	111	113	115	117	119	121	123	125
Number of children	2	4	14	41	83	169	394	669	990	1223	1329
Height(cm)	127	129	131	133	135	137	139	141	143	145
No. of children	1230	1063	646	392	202	79	32	16	5	2

23	15	75	48	59	01	83	72	59	93	76	24	97	08	86	95	23	03	67	44
05	54	55	50	43	10	53	74	35	08	90	61	18	37	44	10	96	22	13	43
14	87	16	03	50	32	40	43	62	23	50	05	10	03	22	11	54	36	08	34
38	97	67	49	51	94	05	17	58	53	78	80	59	01	94	32	42	87	16	95
97	31	26	17	18	99	75	53	08	70	94	25	12	58	41	54	88	21	05	13

23	15	75	48	59	01	83	72	59	93	76	24	97	08	86	95	23	03	67	44
05	54	55	50	43	10	53	74	35	08	90	61	18	37	44	10	96	22	13	43
14	87	16	03	50	32	40	43	62	23	50	05	10	03	22	11	54	36	08	34
38	97	67	49	51	94	05	17	58	53	78	80	59	01	94	32	42	87	16	95
97	31	26	17	18	99	75	53	08	70	94	25	12	58	41	54	88	21	05	13

23	15	75	48	59	01	83	72	59	93	76	24	97	08	86	95	23	03	67	44
05	54	55	50	43	10	53	74	35	08	90	61	18	37	44	10	96	22	13	43
14	87	16	03	50	32	40	43	62	23	50	05	10	03	22	11	54	36	08	34
38	97	67	49	51	94	05	17	58	53	78	80	59	01	94	32	42	87	16	95
97	31	26	17	18	99	75	53	08	70	94	25	12	58	41	54	88	21	05	13

23	15	75	48	59	01	83	72	59	93	76	24	97	08	86	95	23	03	67	44
05	54	55	50	43	10	53	74	35	08	90	61	18	37	44	10	96	22	13	43
14	87	16	03	50	32	40	43	62	23	50	05	10	03	22	11	54	36	08	34
38	97	67	49	51	94	05	17	58	53	78	80	59	01	94	32	42	87	16	95
97	31	26	17	18	99	75	53	08	70	94	25	12	58	41	54	88	21	05	13

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12th Standard English Medium

12th Standard Tamil Medium

11th Standard English Medium

11th Standard Tamil Medium

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12th Business Maths Monthly Test - 2 ( Sampling techniques and Statistical Inference )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Monthly Test - 2 ( Sampling techniques and Statistical Inference )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

___________ is a relative property, which states that one estimator is efficient relative to another.

An estimate of a population parameter given by two numbers between which the parameter would be expected to lie is called an ___________ nterval estimate of the parameter.

Errors in sampling are of

Type II error is

An estimator is a sample statistic used to estimate a

In ___________ the heterogeneous groups are divided into homogeneous groups.

If probability \(P[|\breve { \theta } -\theta |<\varepsilon ]\rightarrow 1\mu \quad as\quad n\rightarrow \infty ',\) for any positive \(\varepsilon \) then \(\breve { \theta } \) is said to _____________ esitimator of \(\theta\).

Type I error is

In simple random sampling from a population of units, the probability of drawing any unit at the first draw is

A_________is one where each item in the universe has an equal chance of known opportunity of being selected.

A __________ of statistical individuals in a population is called a sample.

A random sample is a sample selected in such a way that every item in the population has an equal chance of being included

Which one of the following is probability sampling

A …………. may be finite or infinite according as the number of observations or items in it is finite or infinite.

The method of obtaining the most likely value of the population parameter using statistic is called _____________

Part - B

Generic 2 - Answer All Question

What is confidence interval?

In a sample of 400 population from a village 230 are found to be eaters of vegetarian items and the rest non-vegetarian items. Compute the standard error assuming that both vegetarian and non-vegetarian foods are equally popular in that village?

Explain in detail about the test of significance for single mean

Explain the types of sampling.

Explain in detail about systematic random sampling with example.

Explain the procedures of testing of hypothesis

Part - C

Generic 3 - Answer All Question

A sample of 100 students is chosen from a large group of students. The average height of these students is 162 cm and standard deviation (S.D) is 8 cm. Obtain the standard error for the average height of large group of students of 160 cm?

From the following data, select 68 random samples from the populationof heterogeneous group with size of 500 through stratified random sampling, considering the following categories as strata. Category1: Lower income class -39% Category2: Middle income class - 38% Category3: Upper income class- 23%

Find the sample size for the given standard deviation 10 and the standard error with respect of sample mean is 3.

A server channel monitored for an hour was found to have an estimated mean of 20 transactions transmitted per minute. The variance is known to be 4. Find the standard error.

The standard deviation of a sample of size 50 is 6.3. Determine the standard error whose population standard deviation is 6?

Part - D

Generic 5 - Answer All Question

(i) A sample of 900 members has a mean 3.4 cm and SD 2.61 cm. Is the sample taken from a large population with mean 3.25 cm. and SD 2.62 cm? (ii) If the population is normal and its mean is unknown, find the 95% and 98% confidence limits of true mean.

The mean life time of a sample of 169 light bulbs manufactured by a company is found to be 1350 hours with a standard deviation of 100 hours. Establish 90% confidence limits within which the mean life time of light bulbs is expected to lie.

The mean weekly sales of soap bars in departmental stores were 146.3 bars per store. After an advertising campaign the mean weekly sales in 400 stores for a typical week increased to 153.7 and showed a standard deviation of 17.2. Was the advertising campaign successful?

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From the following data, select 68 random samples from the populationof heterogeneous group with size of 500 through stratified random sampling, considering the following categories as strata.
Category1: Lower income class -39%
Category2: Middle income class - 38%
Category3: Upper income class- 23%

(i) A sample of 900 members has a mean 3.4 cm and SD 2.61 cm. Is the sample taken from a large population with mean 3.25 cm. and SD 2.62 cm?
(ii) If the population is normal and its mean is unknown, find the 95% and 98% confidence limits of true mean.

23	15	75	48	59	01	83	72	59	93	76	24	97	08	86	95	23	03	67	44
05	54	55	50	43	10	53	74	35	08	90	61	18	37	44	10	96	22	13	43
14	87	16	03	50	32	40	43	62	23	50	05	10	03	22	11	54	36	08	34
38	97	67	49	51	94	05	17	58	53	78	80	59	01	94	32	42	87	16	95
97	31	26	17	18	99	75	53	08	70	94	25	12	58	41	54	88	21	05	13

23	15	75	48	59	01	83	72	59	93	76	24	97	08	86	95	23	03	67	44
05	54	55	50	43	10	53	74	35	08	90	61	18	37	44	10	96	22	13	43
14	87	16	03	50	32	40	43	62	23	50	05	10	03	22	11	54	36	08	34
38	97	67	49	51	94	05	17	58	53	78	80	59	01	94	32	42	87	16	95
97	31	26	17	18	99	75	53	08	70	94	25	12	58	41	54	88	21	05	13