In sampling from a large population with б = 12, the standard error of the mean is found to be 3. The size of the sample used is:

• A) 16
• B) 22
• C) 12
• D) 11

Simple random sampling is appropriate, when the units in population are

• A) Homogeneous
• B) Heterogeneous
• C) Not accessible
• D) Accesssble

Interval estimation and confidence interval are:

• A) Different
• B) Same
• C) Independent
• D) Opposite

In repeating sampling, which of the following possess desirable property of being Unbiased?

• A) Sample Mean
• B) Sample proportion
• C) All of above
• D) Sample median

Consider a large population with a mean of 160 and a standard deviation of 25. A random sample of size 64 is taken from this population. What is the standard deviation of the sample mean?

• A) 4.254
• B) 1.256
• C) 2.569
• D) 3.125

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

• A) The method of least square
• B) The method of maximum likelihood
• C) The method of fractional moments
• D) The method of moments

An estimator is said to be efficient if it has

• A) Unbiased estimate
• B) None of these
• C) Both (a) & (b)
• D) Smallest Variance

The central limit theorem states that the mean of the sampling distribution of the means is equal to the population:

• A) Mean
• B) Standard deviation
• C) Random Error
• D) Standard error

A parameter is a ..... quantity.

• A) Constant
• B) Random
• C) Sample
• D) Variable

A randomly selected sample of 400 students at a university with 15-week semesters was asked whether or not they think the semester should be shortened to 14 weeks.46% of the 400 students surveyed answered "yes". Which one of the following statements about the number 46% is correct?

• A) It is a population parameter
• B) It is a standard error
• C) It is a sample statistic
• D) It is a margin of error

The confidence intervals become wide and less precise by

• A) decreasing the sample size
• B) decreasing the level of significance
• C) increasing the sample size
• D) None of these

[Math Processing Error]$${\text{The mean of the sampling distribution of }}\overline x _1 - \overline x _2 {\text{, denoted by }}\mu _{\overline x _1 - \overline x _2 } {\text{is equal to the difference between repective}}$$

• A) Population Proportions
• B) Population Means
• C) Sample Means
• D) Sample Proportions

According{\text{ }}to{\text{ }}emperical{\text{ }}rule,{\text{ }}how{\text{ }}much{\text{ }}data{\text{ }}lies{\text{ }}between\,\mu - 3\sigma \,and\,\mu + 3\sigma \,?

• A) 99.73%
• B) 68.26%
• C) 50%
• D) 95.44%

{\text{The mean of the sampling distribution of }}\overline x _1 - \overline x _2 {\text{, denoted by }}\mu _{\overline x _1 - \overline x _2 } {\text{is equal to the difference between repective}}

• A) Population Proportions
• B) Sample Proportions
• C) Sample Means
• D) Population Means

\[{\text{In hyper geometric distribution; N = number of units in the population, n = number of units in the sample and k = number of successes in the population, then mean of hyper geometric distribution is defined as:}}\]

• A) \[\frac{n}{N}\]
• B) \[n.k\]
• C) \[n\frac{k}{N}\]
• D) \[\frac{k}{N}\]

{\text{In hyper geometric distribution; N = number of units in the population, n = number of units in the sample and k = number of successes in the population, then mean of hyper geometric distribution is defined as:}}

• A) \frac{k}{N}
• B) \frac{n}{N}
• C) n\frac{k}{N}
• D) n.k

\begin{gathered} {\text{If X and Y are two discrete r}}{\text{.v's with joint probability function f (X}}_i ,Y_j ), \ {\text{then the conditional distribution of X given Y is:}} \\ \end{gathered} given by

• A) Both of the above
• B) f\left( {{\text{X}}_i |Y_j } \right){\text{ }} = f\left( {X_i ,{\text{ Y}}_j } \right){\text{ }}/g\left( {X_i } \right)
• C) f\left( {{\text{X}}_i |Y_j } \right){\text{ }} = f\left( {X_i ,{\text{ Y}}_j } \right){\text{ }}/h\left( {Y_j } \right)
• D) None of the above

According{\text{ }}to{\text{ }}emperical{\text{ }}rule,{\text{ }}how{\text{ }}much{\text{ }}data{\text{ }}lies{\text{ }}between\,\mu - 2\sigma \,and\,\mu + 2\sigma \,?

• A) 68.26%
• B) 50%
• C) 99.73%
• D) 95.44%

\[{\text{In a normal distribution how much area lies between }}\mu \pm \sigma \]

• A) 65%
• B) 80%
• C) 68.26%
• D) 75%

{\text{For the Poisson distribution P(X = 1) = }}\frac{{{e^{ - 2}}{2^1}}}{{1!}}{\text{ the mean value is:}}

• A) 0
• B) 2
• C) 3
• D) 1