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# STA301 - Statistics and Probability QUIZ No.02 Discussion Due Date : 15-02-2013

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Attachments:

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Chapter No 27 to 30

Chapter No 33 to 35

Chapter No 40 to 43

Total Chapter 11

Total Quizzes 10

So = 10/11 = 0.90909090909090909090909090909091 = 0.909091% Chance today

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Attachments:

In a chi-square distribution, if Variance is 9 then value of mean will be:

In general, the estimators obtained by the method of moments are ………….

A confidence interval has a specified probability__________ of containing the true value of the parameter.

The precision of an estimator can be increased by decreasing the;

In a Poisson distribution, Maximum Likelihood Estimator (MLE) for meu (u) is equal to:

We can apply method of Maximum Likelihood on:

If b(x, 7, 0.30), the variance of this distribution is:

“The temperatures of patients were checked before and after given a certain medicine.” This is an example of:

Natural pairing of data

Pairing by design

Which of the following must not be a consistent estimator

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Attachments:

Question # 1 of 10 (Start time: 06:44:02 PM)            Total Marks: 1

In the method of moments, how many equations are required for finding two unknown population parameters?

Select correct option:

• 1
• 2
• 3
• 4

Question # 2 of 10 (Start time: 06:45:31 PM)            Total Marks: 1

For statistical inference about the mean of a single population when the population standard deviation is unknown, the degrees for freedom for the t distribution equal n-1 because we lose one degree of freedom by using the:

Select correct option:

Sample mean as an estimate of the population mean

Sample size as an estimate of the population size

Sample proportion as an estimate of the population proportion

Sample standard deviation as an estimate of the population standard deviation

Question # 3 of 10 ( Start time: 06:47:31 PM )          Total Marks: 1

An urn contains 4 red balls and 6 green balls. A sample of 4 balls is selected from the urn without replacement. It is the example of:

Select correct option:

Binomial distribution

Hypergeometric distribution

Poisson distribution

Exponential distribution

Question # 4 of 10 ( Start time: 06:48:17 PM )          Total Marks: 1

An estimator is always a:

Select correct option:

Statistic

Random variable

Statistic and Random variable

Parameter

Question # 5 of 10 ( Start time: 06:49:50 PM )          Total Marks: 1

The Chi- Square distribution is continuous distribution ranging from:

Select correct option:

Zero to infinity

Minus infinity to plus infinity

Minus infinity to one

One to plus infinity

Question # 6 of 10 ( Start time: 06:51:10 PM )          Total Marks: 1

In a Geometric distribution, Maximum Likelihood Estimator (MLE) for proportion (P) is equal to:

Select correct option:

Sample mean

Reciprocal of the mean

Sample variance

Reciprocal of the sample variance

Question # 7 of 10 ( Start time: 06:52:45 PM )          Total Marks: 1

Let X be a random variable with binomial distribution, that is (x=0,1,…, n). The Var[X] is:

Select correct option:

P

NP

NP (1-p)

Xnp

Question # 8 of 10 ( Start time: 06:54:23 PM )          Total Marks: 1

ANOVA stands for

Select correct option:

Analysis of variance

Analysis of covariance

Analysis of variables

All above

Question # 9 of 10 ( Start time: 06:55:37 PM )          Total Marks: 1

If an estimator is more efficient then the other estimator, its shape of the sampling distribution will be

Select correct option:

Flattered

Normal

Highly peaked

Skewed to right

Question # 10 of 10 ( Start time: 06:56:34 PM )        Total Marks: 1

How can we interpret the 90% confidence interval for the mean of the normal population?

Select correct option:

There are 10% chances of falling true value of the parameter

There are 90% chances of falling true value of the parameter

There are 100% chances of falling true value of the parameter

All are correct

Question # 1 of 10 ( Start time: 07:03:59 PM )          Total Marks: 1

If a random variable X denotes the number of heads when we toss a fair coin 5 times, the X assumed the values:

Select correct option:

0,1,2,3

1, 2,3,4,5

0, 1, 2,3,4,5

1, 5, 5

Question # 2 of 10 ( Start time: 07:04:50 PM )          Total Marks: 1

Which of the following is most important and most widely used method in point estimation?

Select correct option:

The method of moments

The method of fractional moments

The method of least square

The method of maximum likelihood

The method of maximum likelihood is regarded as the MOST important method of estimation, and is the most widely used method. This method was introduced in 1922 by Sir Ronald A. Fisher (1890-1962).The mathematical technique of finding Maximum Likelihood Estimators is a bit advanced, and involves the concept of the Likelihood Function.

Question # 3 of 10 ( Start time: 07:05:41 PM )          Total Marks: 1

F-distribution is skewed to the

Select correct option:

Right

Left

Right and Left

None of these

Question # 4 of 10 ( Start time: 07:06:49 PM )          Total Marks: 1

As sample size goes up, what tends to happen to 95% confidence intervals?

Select correct option:

They become wider

They become more precise

They become more narrow

They become more precise and narrow

Question # 5 of 10 ( Start time: 07:08:10 PM )          Total Marks: 1

In a Geometric distribution, Maximum Likelihood Estimator (MLE) for proportion (P) is equal to:

Select correct option:

Sample mean

Reciprocal of the mean

Sample variance

Reciprocal of the sample variance

Question # 6 of 10 ( Start time: 07:09:29 PM )          Total Marks: 1

In general, the estimators obtained by the method of moments are ………….

Select correct option:

Biased

Inconsistent

Inefficient

All the above

Question # 7 of 10 ( Start time: 07:10:49 PM )          Total Marks: 1

When we draw the sample with replacement, the probability distribution to be used is:

Select correct option:

Binomial

Hypergeometric

Binomial & hypergeometric

Poisson

Question # 8 of 10 ( Start time: 07:11:28 PM )          Total Marks: 1

ANOVA stands for

Select correct option:

Analysis of variance

Analysis of covariance

Analysis of variables

All above

Question # 9 of 10 ( Start time: 07:12:00 PM )          Total Marks: 1

Suppose 60% of a herd of cattle is infected with a particular disease. Let Y = the number of non-diseased cattle in a sample of size 5. The distribution of Y is:

Select correct option:

Binomial with n = 5 and p = 0.6

Binomial with n = 5 and p = 0.4

Binomial with n = 5 and p = 0.5

Poisson with u = .6

Question # 10 of 10 (Start time: 07:13:04 PM)          Total Marks: 1

The value of chi square can never be:

Select correct option:

Zero

Less than 1

Greater than 1

Negative

Question # 1 of 10 ( Start time: 07:28:04 PM )          Total Marks: 1

We use the Poisson approximation to the binomial when:

Select correct option:

p is 0.01 or less & n is 10

p is 0.05 or less & n is 50

p is 0.04 or less & n is 15

p is 0.02 or less & n is 10

Question # 2 of 10 ( Start time: 07:29:12 PM )          Total Marks: 1

In a Geometric distribution, Maximum Likelihood Estimator (MLE) for proportion (P) is equal to:

Select correct option:

Sample mean

Reciprocal of the mean

Sample variance

Reciprocal of the sample variance

Question # 3 of 10 ( Start time: 07:29:39 PM )          Total Marks: 1

If b(x; 15, 0.75), the mean of this distribution is:

Select correct option:

11.50

11.15

11.20

11.25

Question # 4 of 10 ( Start time: 07:31:02 PM )          Total Marks: 1

Under which of the following circumstances is it impossible to construct a confidence interval for the population mean?

Select correct option:

A normal population with a large sample and a known population variance

A non-normal population with a large sample and an unknown population variance

A normal population with a large sample and a known population variance

A non-normal population with a small sample and an unknown population variance

Question # 5 of 10 ( Start time: 07:32:27 PM )          Total Marks: 1

In completely randomized design (CRD) treatments are assigned to experimental units completely at random, i.e. randomization is done without any?

Select correct option:

Objection

Restriction

Obligation

All above mentioned

Question # 6 of 10 ( Start time: 07:33:42 PM )          Total Marks: 1

If the random variable “X” follows F-distribution with v1 and v2 degrees of freedom, then reciprocal of “X” i.e. “1/X” also follows F-distribution with respective degrees of freedom

Select correct option:

v1

v2

V1 and v2

V2 and v1

Question # 7 of 10 ( Start time: 07:35:02 PM )          Total Marks: 1

The precision of an estimator can be increased by decreasing the;

Select correct option:

Level of significance

Number of parameters

Number of estimators

Size of sample

Question # 8 of 10 ( Start time: 07:36:28 PM )          Total Marks: 1

T-distribtion is applicable in case of

Select correct option:

Independent samples

Dependent samples

Both independent and dependent samples

Non-Normal populations

Question # 9 of 10 ( Start time: 07:37:49 PM )          Total Marks: 1

A consistent estimator will always be a:

Select correct option:

Unbiased estimator

Biased estimator

Unbiased estimator and biased estimator

May or may not be unbiased estimator

Question # 10 of 10 ( Start time: 07:39:15 PM )        Total Marks: 1

Which of the following is desirable for a good point estimator?

Select correct option:

Consistency

Unbiasedness

Efficiency

All of these

Question # 1 of 10 ( Start time: 07:45:27 PM )          Total Marks: 1

Suppose 60% of a herd of cattle is infected with a particular disease. Let Y = the number of non-diseased cattle in a sample of size 5. the distribution of Y is:

Select correct option:

Binomial with n = 5 and p = 0.6

Binomial with n = 5 and p = 0.4

Binomial with n = 5 and p = 0.5

Poisson with u = .6

Question # 2 of 10 ( Start time: 07:45:46 PM )          Total Marks: 1

If b(x; 15, 0.75), the mean of this distribution is:

Select correct option:

11.50

11.15

11.20

11.25

Question # 3 of 10 ( Start time: 07:46:40 PM )          Total Marks: 1

A statistic whose standard deviation decreases with an increase in sample size will be called:

Select correct option:

Unbiased

Consistent

Efficient

Sufficient

Question # 4 of 10 ( Start time: 07:48:04 PM )          Total Marks: 1

F- Distribution has………parameter(s).

Select correct option:

One

Two

Three

No

Question # 5 of 10 ( Start time: 07:49:33 PM )          Total Marks: 1

In an ANOVA test there are 8 observations in each of 3 treatments. The degree of freedom for error in CR design is:

Select correct option:

21

24

14

16

Question # 6 of 10 ( Start time: 07:50:44 PM )          Total Marks: 1

What is the mean and variance of binomial distribution b(x; n, p)?

Select correct option:

Xp and npq

NP and PQ

NP and npq

Zero and one

Question # 7 of 10 ( Start time: 07:52:08 PM )          Total Marks: 1

“A point estimate plus/minus a few times the standard error of that estimate”. This statement represents:

Select correct option:

Confidence interval

Critical region

Acceptance region

Critical value

Question # 8 of 10 ( Start time: 07:53:20 PM )          Total Marks: 1

Mean of F-distribution with V2>2 is

Select correct option:

V1/(V2-2)

V2/(V2-2)

V2/(V1-2)

V1/(V1-2)

Question # 9 of 10 (Start time: 07:54:50 PM)

Which of the following is most important and most widely used method in point estimation?

Select correct option:

The method of moments

The method of fractional moments

The method of least square

The method of maximum likelihood

Question # 10 of 10 (Start time: 07:56:21 PM)

The hypergeometric random variable is a (an):

Select correct option:

Continuous variable

Discrete variable

Undefined

Independent

Which of the following statements is false?

The t distribution is symmetric about zero

The t distribution is more spread out than the standard normal distribution

As the degrees of freedom get smaller, the t-distribution’s dispersion gets smaller

The t distribution is mound-shaped

For statistical inference about the mean of a single population when the population standard deviation is unknown, the degrees for freedom for the t distribution equal n-1 because we lose one degree of freedom by using the:

Sample mean as an estimate of the population mean

Sample standard deviation as an estimate of the population standard deviation

Sample proportion as an estimate of the population proportion

Sample size as an estimate of the population size

In testing the hypotheses Null hypothesis:  mu = 200

Alternative hypothesis:  mu less than 200 the sample mean are found to be 120. The null hypothesis:

Should be rejected

Should not be rejected

Should be rejected only if n > 30

None of the above answers is correct

For a sample of size 20 taken from a normally distributed population with standard deviation equal to 5, a 90% confidence interval for the population mean would require the use of:

t = 1.328

t = 1.729

t = 2.12

z = 1.645

Under which of the following circumstances is it impossible to construct a confidence interval for the population mean?

A non-normal population with a large sample and an unknown population variance

A normal population with a large sample and a known population variance

Non-normal population with a small sample and an unknown population variance

A normal population with a small sample and an unknown population variance

Suppose that a one-tail t test is being applied to find out if the population mean is less than 100. The level of significance is .05 and 25 observations were sampled. The rejection region is:

t > 1.708

t < -1. 711

t > 1.318

t < -1.316

Which of the following is true about the t distribution?

Approaches the normal distribution as its degrees of freedom increase

Assumes the population is normally distributed

It is more spread out than the standard normal distribution

All of the above statements are true

A random sample of size 20 taken from a normally distributed population resulted in a sample variance of 32.  The lower limit of a 90% confidence interval for the population variance would be:

52.185

20.375

20.170

54.931

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:

77.769

72.231

72.727

77.273

Based on sample data, the 90% confidence interval limits for the population mean are LCL = 170.86   UCL = 195.42. If the 10% level of significance were used in testing the hypotheses

Null:  mu = 201

Alt:  mu not equal to 201, the null hypothesis:

Would be rejected

Would not be rejected

Would have to be revised

None of the above

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