Given that the mean of the normal variate X is 10 and the standard deviation is 2, then what will be the z-score of the data point 16 ?

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 : $H_0 : \mu \leq 24$, $H_a : \mu > 24$

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

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:

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 :

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

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