Which of the following statements are TRUE
Note that there may be more than one correct answer; select all that are true.

a)  Like the normal distribution, the t distribution depends on the parameters μ and σ, as well as the degrees of freedom.  
b)  As the sample size increases, the t distribution approaches the standard normal distribution.  
c)  Like the normal distribution, the t distribution is symmetric, but it has heavier tails than the normal distribution.  
d)  The t distribution is centered around 1.  
e)  It is appropriate to use the t distribution when dealing with small sample sizes dr 
1. If the difference between true parameter value and
hypothesised parameter value increases, then the power of
the test increases, so probability of Type II error decreases
and probability of Type I error increases.
Hence, Option (b) is true. (Ans).
It is desirable to have tests with power upto some extent
than tests with low power.
Hence, Option (c) is True. (Ans).
As, the type I error increases, Type II error decreases and
viceversa.
Hence, Option (d) is True. (Ans).
As, the sample size increases, the power of the test
increases. So, Type II error decreases, as,
Power = 1  P(Type II error).
Hence, Option (e) is True. (Ans).
2. tdistribution only depends on the degrees of freedom.
As, the sample size increases, tdistribution approaches
standard normal distribution.
Hence, Option (b) is True. (Ans).
tdistribution is symmetric and it has heavier tails than
normal distribution.
Hence, Option (c) is True. (Ans).
tdistribution is centered around 0. tdistribution is
appropriate to use when the sample size is large.
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