Consider the following hypothesis test:

$H_0: \mu \leq 35$

$H_a: \mu > 35$

A sample of 25 provided a sample mean of 34.65. The population standard deviation is 4. The value of the t-test statistic is

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 :

Which of the following is a statistic ?

Statistical inference is a process through which inference about the population are made based on informations obtained from the:

The following data is available for two independent sample:

Then the value of t-statistic is :

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

A simple random sample consists of five observations 2, 4, 7, 12, 15. The point estimate of the population mean is :