Question

Suppose a random sample of size 22 is taken from a normally distributed population, and the sample mean and variance are calculated to be x¯=5.29  and s2=0.5 respectively.

Use this information to test the null hypothesis H0:μ=5  versus the alternative hypothesis HA:μ>5 .

a) What is the value of the test statistic, for testing the null hypothesis that the population mean is equal to 5?

Round your response to at least 3 decimal places.

b) The p-value falls within which one of the following ranges:

		p-value > 0.10
		0.05 < p-value < 0.10
		0.025 < p-value < 0.05
		0.01 < p-value < 0.025
		p-value < 0.01

i) Is the null hypothesis rejected at the 5% level of significance?

Yes No

ii) Is the null hypothesis rejected at the 1% level of significance?

Yes No

Answer 1

Part a)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 5.29 - 5 ) / ( 0.707107 / √(22) )
t = 1.924

Part b)

P - value = P ( t > 1.9236 ) = 0.034 ( From t table )

0.025 < p-value < 0.05

Part b i)
Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 22-1) = 1.721
t > t(α, n-1) = 1.9236 > 1.721
Result :- Reject null hypothesis

Yes, Null hypothesis is rejected.

Part b ii)

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
Critical value t(α, n-1) = t(0.01 , 22-1) = 2.518
t > t(α, n-1) = 1.9236 < 2.518
Result :- Fail to reject null hypothesis
No, null hypothesis is not rejected.