Question

A sample of size 81 is taken from a population with unknown mean and standard deviation 4.5.  

In a test of H₀: μ = 5 vs. H_a: μ < 5, if the sample mean was 4, which of the following is true?

(i) We would reject the null hypothesis at α = 0.01.

(ii) We would reject the null hypothesis at α = 0.05.

(iii) We would reject the null hypothesis at α = 0.10.

		only (i)
		only (iii)
		both (i) and (ii)
		both (ii) and (iii)
		all of them

Answer 1

Given information

n = 81

Test Statistics :

We find P value using table or technology

P value = 0.0228        ( Using excel =NORMSDIST(-2)   or see the z table at -2 row and 00 column we get this p value)

i) at

P value ( 0.0228) > we fails to reject H0 at 1% level of significance.

ii) at

P value ( 0.0228) < we reject H0 at 5% level of significance.

iii) at

P value ( 0.0228) > we reject H0 at 10% level of significance.

Answer : (ii) and (iii)