(1.) True or False? We can draw Yiwhich are dependent on each other from a population.

(2) True or False?When the expected value of average (sample average) estimated over indefinite number of samples does not equal the population mean, then we say the sample average is a biased estimator of the population mean.

(3) When we look at sampling, which is a better estimator of population average: sample average or the value of the first observation of the sample?

a. sample average

b. first observation

c. both are equally good estimators at all times

d. none of the above

(4) An estimator of population average is determined using sample average as 0.69, with a 95% confidence interval between 0.05 and 1.51. Is the population average expected to be different from zero at 95% confidence interval?

a. No

b. Yes

c. Can't be determined

(5) A random variable x ~ Normal(3, 2). Then its standard normal counterpart 'z' ~Normal(0,1). Then Z = ?

a. (X-2)/3

b. (x-3)/2

c. (x-2)/3

d. (x-3)/2

(6) For a standard normal variable Z~Normal(0,1), the 95% confidence interval can be constructed as:

a. [-1.96, 0]

b. [-1.96, 1.96]

c. [0, 0]

d. [0, 1.96]

(7) When we estimate a 95% confidence interval, we can state that the probability of the random variable to fall outside the interval is:

a. zero

b. 0.025

c. 0.05

d. 0.95

(8) For finding the interval of an estimate from a sample, the issue of selection/ rejection of an appropriate distribution is that:

IZ has population standard deviation in the denominator, which is a given

IIZ itself is not a random variable

IIIt-distribution is a ratio of two random variables

IVt-distribution is a standard normal random variable and therefore it is better suited for samples

a. Ionly

b. I and II only

c. I and III only

d. II and IV only

please explain your answers clearly.thanks