Question

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. Reference: Ref 8-10 You wish to determine whether there is 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. Using a 5% significance level, the conclusion to be drawn is that there is:

statistically significant evidence that the on-time rate is different for the two airlines. not statistically significant evidence that the on-time rate is the same for the two airlines. statistically significant evidence that the on-time rate is the same for the two airlines. not statistically significant evidence that the on-time rate is different for the two airlines.

Answer 1

From the given information,

Let, n₁ = number of flights of airline 1 = 100 and n₂ = number of flights of airline 1 = 100

p₁ = sample proportion of on-time flights outoff 100 flights of airline 1 = 64/100 = 0.64

p₂ = sample proportion of on-time flights outoff 100 flights of airline 2 = 80/100 = 0.80

Let, P₁ = population proportion of on-time flights of airline 1 and

P₂ = population proportion of on-time flights of airline 2

We have to test the hypothesis H₀ : P₁ = P₂   against H₁ : P₁ P₂

Therefore,

Therefore, the test statistic is

Therefore, the value of the test statistic is 2.5198.

Level of significance = 0.05

Therefore, Z_0.025 = 1.96

Since |z| = 2.5198 >  Z_0.025 = 1.96, we reject the null hypothesis at 5% level of significance and conclude that there is statistically significant evidence that the on-time rate is different for the two airlines at 5% level of significance.