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12th Business Maths Monthly Test - 3 ( Sampling techniques and Statistical Inference )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Monthly Test - 3 ( Sampling techniques and Statistical Inference )-Aug 2020

Time : 2.00 Hours

Part - A

Multiple Choice Question - Answer All Question

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

a sample
a population
universe
census

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

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

efficiency
sufficiency
unbiased
consistency

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

efficient
sufficient
unbiased
consistent

An estimator is a sample statistic used to estimate a

population parameter
biased estimate
sample size
census

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

estimation
estimator
biased estimate
standard error.

In ___________ the heterogeneous groups are divided into homogeneous groups.

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

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

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.

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

Which one of the following is probability sampling

purposive sampling
judgment sampling
simple random sampling
Convenience sampling

Any statistical measure computed from sample data is known as ____________

parameter
statistic
infinite measure
uncountable

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

The standard error of sample mean is

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

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

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

hypothesis
statistic
sample
census

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

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

Infinite set
finite subset
finite set
entire set

Part - B

Generic 5 - Answer All Question

A sample of 100 measurements at breaking strength of cotton thread gave a mean of 7.4 and a standard deviation of 1.2 gms. Find 95% confidence limits for the mean breaking strength of cotton thread.

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 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

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 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?

(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.

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