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

Consider the following hypothesis test:-

H₀: μ = 20

H₁: μ ≠ 20

A sample of 40 provided a sample mean of 19. The standard deviation is 3. Then the value of the t-test statistic is:

A 95 % confidence interval states that the population mean is greater than 152 and less than 160. If $\sigma = 15$ and $Z_{0.025} = 1.96$, then what sample size was used in the study?

Which of the following are correct?

(A) A statistical hypothesis is a statement about the population parameter which may be true or false.

(B) In a statistical hypothesis testing procedure, a Type I error is made when the null hypothesis is accepted when it is false.

(C) In a statistical hypothesis testing procedure, a Type II error is made when the null hypothesis is rejected when it is true.

(D) The number of degrees of freedom of a statistic is the number of independent variates used to compute that statistic.

Choose the correct answer from the options given below:

If a sample has 'n' observation $x_1$, $x_2$ ............. $x_n$ with 'm' constraints on these values then degree of freedom of sample statistic is:

If a 95% confidence interval for a population mean was reported to be 132 to 160 and sample standard deviation $\sigma = 50$, then the size of the sample in the study is:

(Given $z_{0.025} = 1.96$)

If a 99% confidence interval states that the population mean is greater than 100 and less than 400. Then the sample mean and margin of error respectively are: