A simple random sample consists of five observations: 2, 4, 6, 7,11, then which of the following are true ?

A. Sample mean = 7.5

B. Sample mean = 6

C. Sample standard deviation = $\sqrt{11}$

D. Sample standard deviation = $\sqrt{11.5}$

Choose the correct answer from the options given below:

T- test : A t- test is a test of difference for parameter data $t = \frac{\overline{x1} - \overline{x2}}{s\sqrt{\frac{1}{n1} + \frac{1}{n2}}}$

Then read the following statements and choose the correct statements

(A) the null hypothesis and the alternative hypothesis have the same viewpoint

(B) In t- test testing the significance of mean value is done, when sample size is small

(C) T - test for two independent groups when variance is equal

(D) Testing is a process used by statisticians to accept or reject the hypothesis

(E) if the value of test statistics is greater than the table values, we do not reject the null hypothesis

Choose the correct answer from the options given below :

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

Five students are selected at random from a school and their weights are found to be 50, 51, 53, 54 and 62. The point estimation of the population mean is:

A simple random sample consists of three observations 1, 3, 5. The point estimate of the population standard deviation is :

From a population having a mean of 20 and standard deviation 2, a random sample of size 64 is taken and its mean is found to be 19.5. The test statistic to test that the sample is taken from the population is

In a survey question for a sample of 250 individuals, 100 students gave response 'good', 60 gave response 'average' and 90 students gave response as 'extra ordinary'. The point estimate of the proportion in the population who respond 'extra ordinary' is: