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

St. Britto Hr. Sec. School - Madurai

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

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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

A ________ is a statement or an assertion about the population parameter.

hypothesis
statistic
sample
census

Errors in sampling are of

Two types
three types
four types
five types

An estimator is a sample statistic used to estimate a

population parameter
biased estimate
sample size
census

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

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

Any statistical measure computed from sample data is known as ____________

parameter
statistic
infinite measure
uncountable

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

a sample
a population
universe
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.

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

An estimator is said to be __________ if it contains all the information in the data about the parameter it estimates.

efficient
sufficient
unbiased
consistent

The standard error of sample mean is

\(\frac { \sigma }{ \sqrt { 2n } } \)
\(\frac { \sigma }{ { n } } \)
\(\frac { \sigma }{ \sqrt { n } } \)
\(\frac { { \sigma }^{ 2 } }{ \sqrt { n } } \)

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

Infinite set
finite subset
finite set
entire set

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

In ___________ the heterogeneous groups are divided into homogeneous groups.

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

Part - B

Generic 2 - Answer All Question

The mean I.Q of a sample of 1600 children was 99. Is it likely that this was a random sample from a population with mean I.Q 100 and standard deviation 15 ? (Test at 5% level of significance)

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 the stratified random sampling with a suitable example.

A sample of 1000 students whose mean weight is 119 lbs(pounds) from a school in Tamil Nadu State was taken and their average weight was found to be 120 lbs with a standard deviation of 30 lbs. Calculate standard error of mean.

What is population?

What is type I error

State any two demerits of systematic random sampling.

Define critical value.

What is sampling distribution of a statistic?
What is an estimator?

What is confidence interval?

What is standard error?

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.

Write short note on sampling distribution and standard error.

Explain the procedures of testing of hypothesis

What is point estimation?

Part - C

Generic 3 - Answer All Question

A die is thrown 9000 times and a throw of 3 or 4 is observed 3240 times. Find the standard error of the proportion for an unbiased die .

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

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%

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.

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?

Using the following Tippett’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 15 houses from Cauvery Street which has 83 houses in total.

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

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

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.

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

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.

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?

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?

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

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?

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