Use the following to answer questions 78 An SRS of 100 fligh

Use the following to answer questions 7-8:

An SRS of 100 flights of a large airline (call this airline 1) showed that 64 were on time. An SRS of 100 flights of another large airline (call this airline 2) showed that 80 were on time. Let p₁ and p₂ be the proportion of all flights that are on time for these two airlines.

Question 7

A 90% confidence interval for the difference p₁ – p₂ is:

Question 7 options:

A)

0.16 ± 0.062.

B)

–0.16 ± 0.103.

C)

–0.16 ± 0.062.

D)

–0.16 ± 0.122.

Question 8

Is there evidence of a difference in the on-time rate for the two airlines? To determine this, you test the hypotheses

H₀: p₁ = p₂, Ha: p₁ p₂.

The P-value of your test of the hypotheses given is:

Question 8 options:

A)

between .10 and .05.

B)

below .001.

C)

between .01 and .001.

D)

between .05 and .01.

Solution

I)
Confidence Interval for Diffrence of Proportion
CI = (p1 - p2) ± Z a/2 Sqrt(p1(1-p1)/n1 + p2(1-p2)/n2 )
Proportion 1
Probability Succuses( X1 )=64
No.Of Observed (n1)=100
P1= X1/n1=0.64
Proportion 2
Probability Succuses(X2)=80
No.Of Observed (n2)=100
P2= X2/n2=0.8
C.I = (0.64-0.8) ±Z a/2 * Sqrt( (0.64*0.36/100) + (0.8*0.2/100) )
=(0.64-0.8) ± 1.64* Sqrt(0.004)
=-0.16-0.103,-0.16+0.103
=[-0.262,-0.058]

Ans: B) –0.16 ± 0.103

II)
Null, No difference in the on-time rate for the two airlines Ho: p1 = p2
Alternate: difference in the on-time rate for the two airlines H1: p1 != p2
Test Statistic
Sample 1 : X1 =64, n1 =100, P1= X1/n1=0.64
Sample 2 : X2 =80, n2 =100, P2= X2/n2=0.8
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.72
Q^ Value For Proportion= 1-P^=0.28
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.64-0.8)/Sqrt((0.72*0.28(1/100+1/100))
Zo =-2.52
| Zo | =2.52
AT 0.05 LOS: Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =2.52 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho

AT 0.1 LOS: Critical Value
The Value of |Z | at LOS 0.1% is 1.645
Hence Value of | Zo | > | Z | and Here we Reject Ho

difference in the on-time rate for the two airlines

A)
between .10 and .05. We have evidence for difference in the on-time rate for the two airlines