Consider the following hypothesis test:

$H_0: \mu \leq 25$

$H_a: \mu > 25$

A sample of 25 provided a sample mean of 27.80. The population standard deviation is 5, then the value of the test statistic is

Consider the following hypothesis test:

$H_0: \mu \leq 12$

$H_a: \mu > 12$

A sample of 25 provided a sample mean $\bar{x} = 14$ and a sample standard deviation $s = 4.32$. If $t_{0.05} = 1.711$, then which of the following is correct?

(A) The test statistic is defined as $t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$.

(B) The value of the test statistic is 1.31.

(C) At $\alpha = 0.05$, the null hypothesis is rejected.

(D) If the value of the t-statistic is less than $t_\alpha$, then null hypothesis is accepted.

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:

Let us suppose that two independent random samples of sizes $n_1$ and $n_2$ has been drawn from the same normal population then degree of freedom of statistic t-distribution is:

The following data are from a random sample: 5,8,10,7,10,14, then the point estimate of the population standard deviation is

The central limit theorem states that the sampling distribution of the sample mean approaches the 'X' distribution, as the sample size gets larger, no matter what the shape of the population is, then 'X' is

The normal distribution is called as standard normal distribution when