Cock and Balls
Chapter 11 – Question 24 (p. 351):
At the .05 significance level, is the number of units produced on the night shift larger?
H0: µ1 ≤ µ2
H1: µ1 > µ2
Z critical value: 1.645 x̄d (µ1): 351 x̄n (µ2): 345 σ^2d: 21 σ^2n: 28
Nd: 54
Nn: 60
Z=(351-345)/SQRT((28^2/60)+(21^2/54))=1.302
Fail to reject the null. Z is less than the critical value; therefore, the number of units produced on the night shift is less than the number of units produced on the day shift.
Chapter 11 – Question 34 (p. 352):
Does this data provide evidence at the .05 significance level that there is a difference in the proportion of humorous ads in British versus American trade magazines?
H0: p1=p2
H1: p1≠p2
Z critical value: 1.960
N1: 270
N2: 203
X1: 56
X2: 52
P1: 56/270=.2074
P2: 52/203=.2561
Pc: (56+52)/(270+203)=.2283
Z=(.2074-.2561)/SQRT((.2283(1-.2283)/270)+(.2283(1-.2283)/203))=1.25
Fail to reject the null. Z is less than the critical value; therefore, there is no difference in the proportion American versus British humorous advertisements in trade magazines.
Chapter 11 – Question 37 (p. 352):
At the .01 significance level, can the manufacturer conclude that the price reduction resulted in an increase in sales?
H0: µ1 ≤ µ2
H1: µ1 > µ2
Z critical value: 2.650 x̄1: 125.235 x̄2: 117.714 s1: 15.094 s2: 19.914
S^2p=(8-1)(15.094)^2+(7-1)(19.914)^2/(8+7-2)=305.708
T=(125.125-117)/SQRT((305.708/8)+(305.708/7))=.819
Fail to reject the null. There is no difference in the mean number sold at the regular price and the mean number sold at the reduced price.
Chapter 11 – Question 38 (p. 352):
At the .01 significance level, is it reasonable to conclude that the modification reduced the number of traffic accidents?
H0: µ1 = µ2
H1: µ1 > µ2
Z critical value: 2.624 x̄1: 7.125 x̄2: 4.625 s1: 2.0310 s2: 2.8253
S^2p=(8-1)(2.031)^2+(8-1)(2.8253)^2/(8+8-2)=6.0536
T=(7.125-4.625)/SQRT((6.0536/8)+(6.0536/8))=2.0322
Fail to
At the .05 significance level, is the number of units produced on the night shift larger?
H0: µ1 ≤ µ2
H1: µ1 > µ2
Z critical value: 1.645 x̄d (µ1): 351 x̄n (µ2): 345 σ^2d: 21 σ^2n: 28
Nd: 54
Nn: 60
Z=(351-345)/SQRT((28^2/60)+(21^2/54))=1.302
Fail to reject the null. Z is less than the critical value; therefore, the number of units produced on the night shift is less than the number of units produced on the day shift.
Chapter 11 – Question 34 (p. 352):
Does this data provide evidence at the .05 significance level that there is a difference in the proportion of humorous ads in British versus American trade magazines?
H0: p1=p2
H1: p1≠p2
Z critical value: 1.960
N1: 270
N2: 203
X1: 56
X2: 52
P1: 56/270=.2074
P2: 52/203=.2561
Pc: (56+52)/(270+203)=.2283
Z=(.2074-.2561)/SQRT((.2283(1-.2283)/270)+(.2283(1-.2283)/203))=1.25
Fail to reject the null. Z is less than the critical value; therefore, there is no difference in the proportion American versus British humorous advertisements in trade magazines.
Chapter 11 – Question 37 (p. 352):
At the .01 significance level, can the manufacturer conclude that the price reduction resulted in an increase in sales?
H0: µ1 ≤ µ2
H1: µ1 > µ2
Z critical value: 2.650 x̄1: 125.235 x̄2: 117.714 s1: 15.094 s2: 19.914
S^2p=(8-1)(15.094)^2+(7-1)(19.914)^2/(8+7-2)=305.708
T=(125.125-117)/SQRT((305.708/8)+(305.708/7))=.819
Fail to reject the null. There is no difference in the mean number sold at the regular price and the mean number sold at the reduced price.
Chapter 11 – Question 38 (p. 352):
At the .01 significance level, is it reasonable to conclude that the modification reduced the number of traffic accidents?
H0: µ1 = µ2
H1: µ1 > µ2
Z critical value: 2.624 x̄1: 7.125 x̄2: 4.625 s1: 2.0310 s2: 2.8253
S^2p=(8-1)(2.031)^2+(8-1)(2.8253)^2/(8+8-2)=6.0536
T=(7.125-4.625)/SQRT((6.0536/8)+(6.0536/8))=2.0322
Fail to