Which of the following statements are correct?

A. The measurable characteristic of a population is called parameter.

B. Sample is a subgroup of members of the population.

C. Population is a collection of all elements having the same characteristics.

D. The difference between a population parameter and a sample statistic is known as sampling error.

Choose the correct answer from the options given below:

A sample of size 9 from a normal population with sample mean $\bar{X} = 15.8$ and population estimated standard deviation $\sigma = 3.21$, then 99% confidence interval for population mean is : $(Use: t_8(0.01) = 3.335)$

A specific characteristic of a sample is known as a

Which of the following are correct?

(A) The central limit theorem (CLT) states that the sampling distribution of the sample approaches a normal distribution as the sample size gets larger, no matter what is the shape of the population distribution.

(B) The measurable characteristic of population is called parameter.

(C) The population focuses on the identification of the characteristic.

(D) The sample makes inference about the population.

Choose the correct answer from the options given below:

Consider the following hypothesis test:-

H₀: μ = 20

H₁: μ ≠ 20

A sample of 40 provided a sample mean of 19. The standard deviation is 3. Then the value of the t-test statistic is:

If 95% confidence interval for the population mean was reported to be 140 to 150 and $\sigma = 25$, then size of the sample used in this study is:

[Given: $Z_{0.025} = 1.96$]

Let two independent random samples of sizes $n_1$ and $n_2$ respectively have been drawn from the same normal population. Let $\overline{X_1}$ and $\overline{X_2}$ be the means and let $s_1$ and $s_2$ be their standard deviations. In order to test whether the the two sample means $\overline{X_1}$ and $\overline{X_2}$ differ significantly or not, the $t$-test statistic is given by