This document discusses one-tailed and two-tailed hypothesis tests. It explains that a one-tailed test looks for an increase or decrease in a parameter, while a two-tailed test looks for any change. If the claim uses words like "increased" or "decreased", it is a one-tailed test, while terms like "change" or "different" indicate a two-tailed test. A one-tailed test has a critical region in one tail, while a two-tailed test has critical regions in both tails. The example given is a one-tailed test comparing civil engineering and B.A. salaries, with the alternative hypothesis that engineering salaries are greater than B.A. salaries.

1. One-tailed or Two-tailed Tests
In Statisticshypothesistesting,weneed to judgewhether itis a one-tailed or atwo-tailed test
so thatwecan findthecritical valuesin tables such asStandardNormal zDistribution Tableand
t DistributionTable.And then,by comparingteststatisticvaluewiththecritical valueor
whether statisticvaluefallsin thecritical region,wemakea conclusion either to rejectthenull
hypothesisor to fail to rejectthenull hypothesis.
Howcan wetell whether itisa one-tailed ora two-tailedtest? Itdependson theoriginalclaim
in thequestion.Aone-tailedtestlooksfor an “increase”or “decrease”in theparameter
whereas a two-tailed testlooks for a “change” (could beincreaseor decrease) in the parameter.
Therefore,if weseewords suchas“increased,greater,larger,improved andso on”,or
“decreased,less,smallerandso on”intheoriginal claimof a question (>,<areusedin H1), a
one-tail testisapplied.If wordssuch as“change,thesame,different/differenceand soon” are
used in theclaimof thequestion(≠is used in H1),a two-tailed testisapplied.
In a one-tailed test,thecritical regionhasjustonepart (thegreen areabelow).Itcan bea left-
tailed testor a right-tailed test.Left-tailed test:Thecritical regionisin theextremeleftregion
(tail)under thecurve.Right-tailed test:Thecritical regionisin theextremerightregion(tail)
under thecurve.
rcriticalregion critical region
Left-tailed test Right-tailed test
Sign used in H1: ˂ Sign used in H1: >

2. In two-tailed test,the critical region hastwo parts(thered areasbelow)which are in the two
extreme gerions (tails)underthecurve.
Two-tailed test
Sign used in H1:≠
Example:
Thetrue valueof onetypeof degreeordiplomacannotbequantitatively measured,butwecan
measureitsrelativeimpacton starting salary.GraduatesfromQuebecuniversitieswith a B.A.or
B.Sc. degreehavea mean annual startingsalary of $28,300.Sixty-fiveQuebecgraduateswith a
civil engineering degreearerandomly selected.Theirstarting salarieshavea meanof $36,300.
If thestandard deviation is$1670,usea 0.01level of significanceto testthe claimthatQuebec
graduateswith a civil engineeringdegreehavea mean startingsalarythatis greaterthanthe
mean forgraduateswith a B.A.orB.Sc.degreefromQuebec.
The underlined partof thequestionaboveistheoriginal claimof thisquestion. Thewords
“greater than”showthatitis a one-tailed (righttail) testandthesignusedin H1 is“>”.Thenull
hypothesisand thealternativehypothesisare:
H0: µ = 28,300
H1: µ > 28,300
Note:In MATH1257 ElementaryStatistics,wealwaysuse“=”sign forthenull hypothesisand
the sign of thealternativehypothesisisbasedon theoriginal claimof thequestion. In PSYC
2126 & 2127,weneed to decideon thesymbol used in alternativehypothesisdepending on the

3. original claimof thequestion first,and then theoppositesymbol will beused in null hypothesis.
So,the null hypothesisand alternativehypothesisshouldbe:
H0: µ ≤ 28,300
H1: µ > 28,300