12th Business Maths Weekly Test - 1 ( Sampling techniques and Statistical Inference )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 1 ( Sampling techniques and Statistical Inference )-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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

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

A finite subset of statistical individuals in a population is called __________

a sample
a population
universe
census

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

An estimator is a sample statistic used to estimate a

population parameter
biased estimate
sample size
census

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.

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

efficiency
sufficiency
unbiased
consistency

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

estimation
estimator
biased estimate
standard error.

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

Part - B

Generic 2 - Answer All Question

What is statistic?

Define level of significance

What is single tailed test.

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?

Using the following 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 three digit numbers which are even numbers.

A sample of 100 items, draw from a universe with mean value 4 and S.D 3, has a mean value 63.5. Is the difference in the mean significant?

Part - C

Generic 3 - Answer All Question

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

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 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.

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

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%

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

The wages of the factory workers are assumed to be normally distributed with mean and variance 25. A random sample of 50 workers gives the total wages equal to Rs. 2,550. Test the hypothesis \(\mu\)=52, against the alternative hypothesis \(\mu\)=49 at 1% level of significance.

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.

An ambulance service claims that it takes on the average 8.9 minutes to reach its destination in emergency calls. To check on this claim, the agency which licenses ambulance services has them timed on 50 emergency calls, getting a mean of 9.3 minutes with a standard deviation of 1.6 minutes. What can they conclude at the level of significance
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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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

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

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

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12th Business Maths Weekly Test - 1 ( Sampling techniques and Statistical Inference )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 1 ( Sampling techniques and Statistical Inference )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

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

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.

A finite subset of statistical individuals in a population is called __________

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

An estimator is a sample statistic used to estimate a

Type I error is

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

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

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.

Part - B

Generic 2 - Answer All Question

What is statistic?

Define level of significance

What is single tailed test.

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?

A sample of 100 items, draw from a universe with mean value 4 and S.D 3, has a mean value 63.5. Is the difference in the mean significant?

Part - C

Generic 3 - Answer All Question

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.

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%

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

The wages of the factory workers are assumed to be normally distributed with mean and variance 25. A random sample of 50 workers gives the total wages equal to Rs. 2,550. Test the hypothesis \(\mu\)=52, against the alternative hypothesis \(\mu\)=49 at 1% level of significance.

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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Tamilnadu Stateboardszs - Class

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%

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