Question

3. Suppose you are testing H0 : = 10 vs H1 : 6= 10: The sample is small (n = 5) and the data come from a normal population. The variance, 2, is unknown. (a) Find the critical value(s) corresponding to = 0:10. (b) You find that t = -1.78. Based on your critical value, what decision do you make regarding the null hypothesis (i.e. do you Reject H0 or Do Not Reject H0)?

Answer 1

3)

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 18

H_a : 18

n = 5

df = n - 1 =5 - 1 = 4

t = -1.78

= 0.10

/ 2 = 0.10 / 2 = 0.05

t _,df = t_{0.05 ,4} = +/-2.132

Critical value = +/-2.132

Test statistic < critical value

Fail to reject the null hypothesis (H0)