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 :

Which of the following statements are true ?

(A) Central limit theorem states that the sampling distribution of the mean $(\bar{x})$ approaches a normal distribution as the sample size increases.

(B) As per Central Limit Theorem, when the sample size increases, the mean $(\bar{x})$ for the data becomes closer to the mean of overall population.

(C) The shape of t-distribution does not depend on degree of freedom.

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:

Consider the following hypothesis test : $H_0 : \mu \leq 24$, $H_a : \mu > 24$

A sample of 64 provided a sample mean of 24.3 . The population standard deviation is 2. The value of the test statistic is :

Which of the following is not a statistic ?

Match List - I with List - II.

Choose the correct answer from the options given below :

Consider the following hypothesis test :

$\mu_o : \mu \leq 26$

$\mu_a : \mu > 26$

A sample of 36 is provided with a sample mean of 25.75. The population standard deviation is 3. The value of the test statistic is :