Question

Suppose for a certain population we do not know the value of population standard deviation (σ), and we want to test: H0: μ ≥ 30 against Ha: μ < 30. We are going to perform the test using a sample of size 43.

What assumptions do we need about population distribution?

A. Since sample size is small, we assume the population is normally distributed.

B. Since sample size is sufficiently large, we do not need any assumption about population distribution.

C. Without knowing the value of [(x)] and σ, it is not possible to make any assumption.

D. Since the value of population standard deviation is unknown, we do not need any further assumption.

p-value can be computed as follows: (select the correct method)

A.  2P(t ≥ |T|), where d.f. of t-distribution is 42.

B. P(t ≥ T), where d.f. of t-distribution is 42.
C. 2P(standard normal ≥ |Z|)
D. P(standard normal ≥ Z)
E. P(t ≤ T), where d.f. of t-distribution is 42.
F. P(standard normal ≤ Z)

Suppose our significance level α = 0.091 and the p-value = 0.097. If we make decision on the basis of these information, and if the true value of μ = 27, then what type of error do we make?

A. Type II error.
B. No error in the decision.
C. Without knowing the value of [(x)] and σ, it is not possible to say anything about error type.
D. Type I error.

Answer 1

Answee:-

(1) Since sample size n = 43 is sufficiently large hence it is normally distributed. Hence

Since sample size is sufficiently large, we do not need any assumption about population distribution.

Hence option (B) is correct choice.

(2) Since for t distribution ; p-value = P(t ≥ T) with (n-1) degree of freedom. Hence

P(t ≥ T), where d.f. of t-distribution is 42.

Hence option (B) is correct choice.

(3) Since p-value = 0.097 is greater than level of significance 0.091 . So we do not reject null hypothesis.

If we make a decision it will be Type 1 error.

Hence Type 1 error is correct choice.

Option(D) is correct.