TESTING HYPOTHESIS ABOUT MEANS

Transcription

1 TESTING HYPOTHESIS ABOUT MEANS PROBLEM : TESTING HYPOTHESIS ABOUT A POPULATION MEAN Norepiephrie (alo referre to a arealie) i a i a hormoe a eurotramitter ue a a rug to treat cariac arret a other cariac yrhythmia reultig i imiihe or abet cariac output. It i fou a ampule of ml a cotai mg of active ubtace. O a give proucer, there i ome variatio from o ampule to aother becaue the fillig machiery i ot work properly. The itributio of the cotet i ormal with taar eviatio of σ = A reearch wa oe i orer to meaure the cotet of 0 ampule a the reult are a follow: I it covicig eviece that the mea cotet of Norepiephrie of ampule i le tha the aertie ml? Thik about whether your hypothee are oe ie or two ie!!! Thi will affect the way you calculate probabilitie!! 3. What i the ample ize? 4. Fi the mea of the ample a it aociate cofiece iterval: m = 95% CI = Hit: The formula for arithmetic mea i m = x i σ The formula for 95% cofiece iterval for mea i: m ± Calculate the z tet tatitic for thi ample (the value of z for the ample allow u to perform a probability calculatio to tet the igificace of thi fiig agait the H 0 ) z = m μ i= Hit: The formula for the z tet tatitic i: z = σ 6. Iterpret from tatitical poit of view the obtaie reult. 7. So, i thi covicig eviece that the mea cotet of ampule are le tha the impoe ml? - -

2 PROBLEM 2: ONE SAMPLE T TEST Occupatioal meicie i a relatively ew fiel i meicie, whereby pecific health hazar are ietifie for particular occupatio. Oe topic of recet iteret i the effect of fire fightig o pulmoary fuctio. Suppoe a group of 26, year ol male fire fighter are ietifie a chage i their pulmoary fuctio over a 5 year perio i meaure. Over 5 year it i fou that the fire fighter have a mea eclie i force expiratory volume (FED, the volume of air expelle i eco) of 0.27 litre with a ample taar eviatio of 0.32 litre. Ca ay cocluio be raw about the occupatioal expoure if the expecte chage over 5 year i 0.0 litre i ormal male i thi age group? Aume that the eclie i FEV i ormally itribute with mea μ a ukow variace σ 2. Thik about whether your hypothee are oe ie or two ie!!! Thi will affect the way you calculate probabilitie!! 3. What i the ample ize? 4. Fi the mea value of the ample: m = the populatio: μ = 5. Fi a 95% cofiece iterval for the appropriate parameter. Iterpret your reult. 95% CI = The formula for 95% cofiece iterval for mea i: m ± Calculate the t tet tatitic for thi ample: t = m μ Hit: The formula for the z tet tatitic i: t = 6. Iterpret from tatitical poit of view the obtaie reult. 7. So, 5 year occupatioal expoure lea to ecreae i the force expiratory volume compare with reuctio i ormal male? - 2 -

3 PROBLEM 3: INDEPENDENT SAMPLES AND KNOWN POPULATION VARIANCES NORMAL TEST The alkaliity (mg/l) of water i the upper reache of Someşului Cal river i kow to be ormally itribute with a taar eviatio of 0 mg/l. Alkaliity reaig i the lower reache of the Someşului Cal river i alo kow to be ormally itribute with a taar eviatio of 5 mg/l. Te alkaility reaig are mae i the upper reache of Someşului Cal a twelve i the lower reache with the followig reult Upper Lower Ivetigate at a 5% igificace level the claim that the true alkaliity of water i the lower reache of the river i greater tha that i the upper reache. 3. Fi the mea of alkaliity i upper a lower reache of the river: m = m 2 = Hit: The formula for arithmetic mea i m = x i i= 4. Sigificace level: α = 5. z critical: If calculate z 2.09 reject H Calculate the z tet tatitic for thi ample (the value of z for the ample allow u to perform a probability calculatio to tet the igificace of thi fiig agait the H 0 ) z = (m m 2) Hit: The formula for the z tet tatitic i: z = Iterpret from tatitical poit of view the obtaie reult. 8. So, alkaliity of water i the lower reache of the river i greater tha that i the upper reache? - 3 -

4 PROBLEM 4: INDEPENDENT SAMPLES AND UNKNOWN BUT EQUAL POPULATION VARIANCES T TEST Suppoe a group of 8, year ol male mokig fire fighter are ietifie; thi ample have a mea ytolic bloo preure of 35 mmhg a a ample eviatio of 0 mmhg. A ample of year ol male o mokig fire fighter were imilarly ietifie who have mea ytolic bloo preure of 25 mmhg a a taar eviatio of 0 mmhg. Ivetigate the ifferece betwee mea of ytolic bloo preure of thee two ample. 3. What are the ample ize? = 2 = 4. Sigificace level: α = 0.05 m = m 2 = 5. t critical = Calculate the t tet tatitic for thi ample: t = (m m 2) Hit: The formula for the z tet tatitic i: t = Iterpret from tatitical poit of view the obtaie reult. 8. So, the mea of ytolic bloo preure of mokig fire fighter i igificatly ifferet compare to the omokig fire fighter? - 4 -

5 PROBLEM 5: PAIRED SAMPLES T TEST A tuy wa couct i orer to ae a aily therapeutic chema for treatmet of ferriprive aemia (Fe eficiecy) i ewbor chil. There were iclue ito the tuy 0 breat fee ewbor from urba eviromet. The biochemical expreio of the ferriprive aemia i hemoglobi bloo level expree i mg/l. The ata were collecte at baelie a after 3 moth of treatmet a are preete i the table below: Hemoglobi (mg/l) baelie Hemoglobi (mg/l) 3 moth of treatmet Wa the treatmet efficiet? 3. Compute the ifferece betwee baelie a 3 moth etermiatio of hemoglobi level: Hemoglobi (mg/l) baelie Hemoglobi (mg/l) 3 moth of treatmet Sigificace level: α = Critical regio for two taile tet: egree of freeom = 9; t > Summarize the ifferece: = = Formula: t = = ( ) / /( ) = i i= i= 7. Iterpret from tatitical poit of view the obtaie reult. 8. So, wa the treatmet efficiet? i 2-5 -