Hypothesis Testig
A Statistical hypothesis is a cojecture about a populatio parameter. This cojecture may or may ot be true. The ull hypothesis, symbolized by H 0, is a statistical hypothesis that states that there is o differece betwee a parameter ad a specific value or that there is o differece betwee two parameters.
The alterative hypothesis, symbolized by H, is a statistical hypothesis that states a specific differece betwee a parameter ad a specific value or states that there is a differece betwee two parameters.
Steps i Hypothesis Testig. Stated the hypothesis ( H 0 ad H ). Stated the level of sigificace (α) 3. Determie the test statistic 4. Compute the test statistic (Z test or t test ) 5. Determie the critical regio 6. Make a decisio (reject H 0 or accept H 0 ) 7. Summarize the result
Kids of Hypothesis Test Cocerig Differece Betwee Two Meas. Two-tailed test H 0 : μ μ = μ 0 H : μ μ μ 0 critical regio critical regio (reject H 0 ) (reject H 0 ) ocritical regio (accept H 0 ) Z Z H 0 is accepted if Z Ztest Z
Kids of Hypothesis Test Cocerig Differece Betwee Two Meas. Right-tailed test H 0 : μ μ μ 0 H : μ μ > μ 0 ocritical regio (accept H 0 ) critical regio (reject H 0 ) Z α H 0 is accepted if z test < z α
Kids of Hypothesis Test Cocerig Differece Betwee Two Meas 3. Left-tailed test H 0 : μ μ μ 0 H : μ μ < μ 0 critical regio (reject H 0 ) ocritical regio (accept H 0 ) - Z α H 0 is accepted if z test > - z α
Statistics For Test Cocerig Differece Betwee Two Meas The statistics test used for hypothesis test cocerig differece betwee two meas are:
with the If. (0,) the If (0,). ) ( 0 ) ( 0 0 0 s s s t s X X t s s t s s X X t N X X Z N X X Z p p test test test test
Example. The marketig maager of a braded cosmetics stated that there is o sigificat differece o the volume of their average sale every moth at Market A ad Market B. To prove that statemet, sample for the volume of the average sale at those two markets withi moths is chose radomly. From that samplig, it is kow that at the Market A, the volume of average for each moth is 36 uits with a stadard deviatio of 0, while at the Market B, the volume of average for each moth is 00 uits with a stadard deviatio of 30 uits. Test at the 5% level of sigificace whether that sample support the statemet that there is o differece of the volume of their sale at the two markets.
SOLUTION. Hypothesis H 0 : µ - µ = 0 H : µ - µ 0. Level of sigificace: 5% 3. Statistics Test (?) 4. Computatio t test = 3,458 5. Critical Regio t table = ±,074 6. Decisio: reject H 0 7. Coclusio: the average sale at Market A is ot equal to the average sale at Market B.
EXAMPLE Forty employer of Compay A ad 36 employer of Compay B are chose radomly as the sample to test a hypothesis that the average salary per day i Compay A is higher tha the average salary per day i Compay B. Based o that sample, the average salary per day i Compay A is $80,0 with stadard deviatio $,6 ad i Compay B is $78, with stadard deviatio $,. Decide = 5% whether the sample support the hypothesis that the average salary per day i Compay A is higher tha the average salary per day i Compay B.
SOLUTION. Hypothesis H 0 : µ - µ 0 H : µ - µ > 0. Level of Sigificace: 5% 3. Statistics Test (?) 4. Computatio Z test = 4,68 5. Critical Value Z table =,645 6. Decisio: reject H 0 7. Coclusio: the average salary i Compay A is higher tha the average salary i Compay B.
HOMEWORK Moder Elemetary Statistics (Joh E. Freud & Bejami M. Perles) Page 34 Number.36,.37,.47,.48
.36 Radom samples showed that 40 executives i the isurace idustry claimed o the average 9.4 busiess luches as deductible biweekly expeses, while 50 bak executives claimed o the average 7.9 busiess luches as deductible biweekly expeses. If, o the basis of collateral iformatio, it ca be assumed that σ = σ =3.0 for such data, test at the 0.05 level of sigificace whether the differece betwee these two sample meas is sigificat.
.37 Rework Exercise.36, usig the sample stadard deviatios s =3.3 ad s =.9 istead of the assumed values of σ ad σ.
.47 To test the claim that the resistace of electric wire ca be reduced by more tha 0.050 ohm by alloyig, 5 values obtaied for alloyed wire yielded a average of 0.083 ohm ad a stadard deviatio of 0.003 ohm, ad 5 values obtaied for stadard wire yielded a average of 0.36 ohm ad a stadard deviatio o 0.00 ohm. Use the level of sigificace 0.05 to determie whether the claim has bee substatiated.
.48 Followig are measuremets of the wig spa of two varieties of sparrows i millimeters. Variety : 6 59 54 76 65 64 45 57 8 Variety : 47 80 53 35 53 57 4 38 6 Assumig that the coditios uderlyig the two-sample t test ca be met, test at the 0.05 level of sigificace whether he differece betwee the meas of these two radom samples is sigificat.
SUP o page 79 umber 5 From a populatio, 0 boys ad 0 girls are radomly chose to test which group is more careful i solvig mathematics problems. Their scores of carefuless are described as follows. Boys 8.5 7.6 6.7 8.6 5.9 4.5 5.8 9. 7.8 6.5 Girls 7.8 9.6 8.9 7.5 6.4 3.4 5.9 8.8 9. 8.7 What is the coclusio of that study if the level of sigificace is 5%.
SUP o page 79 umber 6 Followig is the data of a pre-test ad posttest of studets (as the samples) Pre-test 6 7 5 9 8 7 5 6 4 3 8 6 Post-test 7 8 6 9 7 6 6 7 5 4 8 7 Use 5% of level of sigificace to test the assumptio that the post-test is better tha the pre-test.
HOMEWORK Read ad study about Oe Way Aalysis Of Variace ad try to solve problems umber 5.8 ad 5.9 o page 374