Question

A simple random sample of 100 flights of a large airline (Airline A), showed that 80 were on time. A simple random sample of 100 flights of another large airline (Airline B) showed that 64 were on time. Let p1 and p2 be the proportion of all flights that are on time for airline A and airline B, respectively. Is there evidence of a significant difference in the on-time rate for the two airlines? To determine this, test the appropriate hypotheses using the P-value approach, detail all the steps and use alpha=0.05

Answer 1

a)

Hypothesis-

H0: p1 = p2

Ha: p1 p2

Sample proportion 1 = 80/100 = 0.80

Sample proportion 2 = 64/100 = 0.64

Pooled proportion p* = (x1+x2) / n1 + n2) = (80+64) / (100+100) = 0.72

b)

Test statistics

z = (1 - 2) / Sqrt [ p*( 1- p*) * ( 1 / n1 + 1/ n2) ]

= ( 0.80 - 0.64) / Sqrt [ 0.72 * 0.28 * ( 1 / 100 + 1 / 100) ]

= 2.52

This is test statistics value.

c)

Rejection region -

Two tailed critical value at 0.05 level = -1.96 , 1.96

Reject H0 if z < -1.96 , or z > 1.96.

d) Decision-

Since test statistics falls in rejection region, we have sufficient evidence to reject H0.

e)

p-value-

p-value = 2 * P( Z > z)

= 2 * P( Z > 2.52)

= 2 * 0.0059

= 0.0118

f)

Conclusion -

We conclude at 0.05 level that we have enough evidence to support the claim that there is

significant difference between on-time rate for the two airlines.