Question

An airport official wants to prove that the proportion of delayed flights for Airline A (denoted as p1) is less than the proportion of delayed flights for Airline B (denoted as p2). Random samples for both airlines after a storm showed that 51 out of 200 flights for Airline A were delayed, while 60 out of 200 of Airline B's flights were delayed. If the null hypothesis is p1 – p2 = 0, what is (are) the critical value(s) at .05 significance level?

Group of answer choices

z = 1.645

z = – 1.96 and +1.96

None of the answers is correct

z = -1.645

Answer 1

Solution:

Given data

x1 = 51

n1 = 200

x2 = 60

n2 = 200

p̂1 = x1/n1

p̂1 = 51/200

p̂1 = 0.255

p̂2 = x2 /n2

p̂2 = 60/200

p̂2 = 0.3

To state the null and alternative hypothesis:

null hypothesis H0 : p1 – p2 = 0,

Alternative hypothesis Ha : p1 – p2 < 0

This is "left - tailed" test.

To find the critical value(s) at 0.05 significance level:

The z-critical value for a left-tailed test, for a significance level of = 0.05 is

zc​=−1.645

Answer: z = -1.645

Therefore the "Option -d" is the correct answer.