If the sample size is 45, then the degree of freedom is equal to

Which of the following are the assumptions underlying the use of t-distribution?

(A) The variance of population is known.

(B) The samples are drawn from a normally distributed population.

(C) Sample standard deviation is an unbiased estimate of the population variance.

(D) It depends on a parameter known as degree of freedom.

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When the two independent small samples of sizes $n_1$ and $n_2$ with means $\bar{x}_1$ and $\bar{x}_2$ respectively are drawn from populations with identical population variances, the test-statistic is computed as

Match List-I with List-II

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The point estimate of the population standard deviation as per the below mentioned data from a simple random sample 6,10,15,12,9,8 will be :-

Which of the following are true ?

(A) If the mean of a normal variate is 12 and standard deviation is 4, then the Z-score of data point 20 is 2.

(B) Mean of the numbers obtained on throwing a die having '1' on three faces, '2' on two faces and '5' on one face is 3.

(C) If the variance of a Poisson's distribution is 2, then $P(X=0)=\frac{1}{e^2}$.

(D) For a binomial distribution, mean = 9 and the standard deviation is $\frac{3}{2}$, then the number of trials is 12.

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The normal distribution is called as standard normal distribution when