Question

Which of the following statements are TRUE

Note that there may be more than one correct answer; select all that are true.

	a)	The power of a test is only influenced by the hypothesized parameter value, and not the true parameter value.
	b)	For a two-sided alternative hypothesis, as the difference between the true parameter value and the hypothesized parameter value increases, the probability of a Type I error increases.
	c)	It is desirable to have tests with high power, versus having tests with low power.
	d)	Type I and Type II error are complementary events.
	e)	As the sample size increases, the probability of Type II error decreases.

	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

Answer 1

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

vice-versa.

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. t-distribution only depends on the degrees of freedom.

As, the sample size increases, t-distribution approaches

standard normal distribution.

Hence, Option (b) is True. (Ans).

t-distribution is symmetric and it has heavier tails than

normal distribution.

Hence, Option (c) is True. (Ans).

t-distribution is centered around 0. t-distribution is

appropriate to use when the sample size is large.