Which of the following points describe the concept of population in inferential statistics ?

A. It is a collection of all elements having same characteristics.

B. A survey done on the total population is not accurate.

C. Population focuses on the identification of the characteristic.

D. Population focuses on drawing inference about the sample.

Choose the correct answer from the options given below:

If the following data is obtained from a simple random sample:

6, 7, 9, 10, 11, 17

Then the point estimate of population standard deviation is:

If $95 \%$ confidence interval for the population mean was reported to be $160$ to $170$ and $\sigma=25$, then size of the sample used in this study is: (Given $\mathrm{Z}_{0.025}=1.96$ )

The following data is from a simple random sample :

$15,23, x, 37,19,32$

If the point estimate of the population mean is $23$, then the value of $x$ is :

A machine has been producing steel tubes of mean inner diameter of 2 cm. A sample of 10 tubes gives an inner diameter of 2.01 cm and a standard deviation of 0.063 cm. Test the hypothesis that the machine is working in the proper order at 5 % level of significance and answer, which of the following statements are correct?

[Given that : t₉(0.05) = 2.262]

(A) The value of the test statistic is t = 0.476.

(B) The null hypothesis is rejected at 5 % level of significance.

(C) The null hypothesis is accepted at 5 % level of significance.

(D) The degree of freedom is 10.

Choose the correct answer from the options given below:

Which of the following statements are correct about the "Central Limit Theorem"?

(A) The sampling distribution of the sample mean approaches the normal distribution as the sample size gets larger.

(B) A sample size of 30 or more is considered to be sufficient to hold the "Central Limit Theorem".

(C) As the sample size becomes larger, the prediction of characteristics of the population becomes more accurate.

(D) The sampling distribution of the sample mean approaches a bell shaped curve as the sample size gets larger.

Choose the correct answer from the options given below:

A 95% confidence interval for a population mean was reported to be 152 to 160. If standard deviation $\sigma = 15$ . Then the sample size is : ($Z_{0.025}$=1.96)