To test the claim (at 1% significance) that the proportion of voters who smoked cannabis frequently was lower among conservatives, the hypotheses were In the hypothesis test about cannabis use by conservatives and liberals, the P-value is extremely small. Which of the following errors is possible in this situation?

A. Type I only
B. Type II only
C. Type I and Type II
D. Neither Type I nor Type II

When testing a hypothesis, the largest value of probability which is acceptable for a type I error is called the level of signiﬁcance of the test. The level of signiﬁcance is indicated by the symbol α (alpha) and the levels commonly adopted are 0.1,0.05,0.01, 0.005 and 0.002.

A level of signiﬁcance of 1%,say,0.01 means that 1 times in 100 the hypothesis has been rejected when it should have been accepted.

In signiﬁcance tests, the following terminology is frequently adopted:

(i) if the level of signiﬁcance is 0.01 or less, i.e. the conﬁdence level is 9 9% or more, the results are considered to be highly signiﬁcant, i.e. the results are considered likely to be correct,

(ii) if the level of signiﬁcance is 0.05 or between 0.05and0.01,i.e.theconﬁdencelevelis95%or between 95% and 99%, the results are considered to be probably signiﬁcant, i.e. the results are probably correct,

(iii) if the level of signiﬁcance is greater than 0.05, i.e. the conﬁdence level is less than 95%, the results are considered to be not signiﬁcant, that is, there are doubts about the correctness of the results obtained.