The assumption opposite of what is made in the null hypothesis is known as the _________ hypothesis.

For testing the difference between the means of two samples, the following data is available :

The value of the t-statistics is :

From a sample of 5 items having values 2, 4, 6, 7, 6, the unbiased estimates of the population mean and the standard deviation are:

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 :

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 :

In the formula for Z-test statistic $Z = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}}$, mark the incorrect statement.

A simple random sample consists of four observations 7, 8, 10, 7. The point estimate of population standard deviation is :