Several studies have shown a link between iron depletion without anemia (IDNA) a

Question

Several studies have shown a link between iron depletion without anemia (IDNA) and physical performance. In one recent study, the physical performance of 23 female collegiate rowers with IDNA was compared with 23 female collegiate rowers with normal iron status. Several different measures of physical performance were studied, but we'll focus here on training-session duration. Assume that training-session duration of female rowers with IDNA is Normally distributed with mean 56 minutes and standard deviation 12 minutes. Training-session duration of female rowers with normal iron status is Normally distributed with mean 67 minutes and standard deviation 19 minutes

(a) Use software to find the probability (±± 0.001) that the mean duration of the 23 rowers with IDNA exceeds 62 minutes?

P(x¯>62) =

(b) Use software to find the probability (±± 0.001) that the mean duration of the 23 rowers with normal iron status is less than 62 minutes?

P(x¯<62) =

(c) Use software to find the probability (±± 0.001) that the mean duration of the 23 rowers with IDNA is greater than the mean duration of the 23 rowers with normal iron status?

P(x¯IDNAx¯Normal>0) =

Explanation / Answer

a) std error of mean =std deviation/(n)1/2 =12/(23)1/2 =2.50

threfore P(x¯>62) =P(Z>(62-56)/2.50)=P(Z>2.3979)=0.008

b)

std error of mean =std deviation/(n)1/2 =19/(23)1/2 =3.96

P(X<62)= =P(Z<(62-67)/3.96)=P(Z<-1.262) =0.103

c) here mean difference =56-67 =-11

and std error of difference =(122/23+192/23)1/2 =4.6858

therefore P(x¯IDNAx¯Normal>0) = P(Z>(0-(-11)/4.6858)=P(Z>2.3475)=0.009

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.