State whether the following statements are True or False. Give reasons in support of your answer:

(i) is a random sample of size 5 taken from an Exponential distribution, then estimator T₁ is more efficient than T2.

(ii)  are two estimators of the parameter such that Var(T₁) = 1/n and Var(T₂₎ = n then T₁ is more efficient than T₂.

(iii) A 95% confidence interval is smaller than a 99% confidence interval.

(iv) If the probability density function of a random variable X follows F-distribution is

then degrees of freedom of the distribution will be (2,2).

(v) A patient suffering from fever reaches to a doctor and suppose the doctor formulates the hypotheses as

Ho: The patient is a chikungunya patient

H₁: The patient is not a chikungunya patient

If the doctor rejects Ho when the patient is actually a chikunguniya patient, then the doctor commits type II error.

(i) False
Reason: Without specific definitions or variances of estimators T₁ and T₂, efficiency cannot be compared. Efficiency is determined by the variance of unbiased estimators. If T₁ has a _____ ________ ________ ______ ________ _________.
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