An airline claims that 75% of its flights depart on time

Question

An airline claims that 75% of its flights depart on time. A sample of 100 flights was examined and it was determined that 73% left on time. If the goal is to test whether less than 75% of the flights depart on time, what is the value of the calculated test statistic at the 5% level of significance?
a.
z = –0.460
b.
z = –0.046
c.
z = 0.046
d.
z = 0.460

Answer 1

This problem is concerned with a single sample with sample size > 30 and the dataset is satisfying parametric assumptions, hence the appropriate statistical test would be single sample z-test. The step by step sequence for z - test is as follows:

The question provides:

p₀ = 0.75

p̂ = 0.73

n = 100

Formula to calculate z :

z = (p̂ - p₀) / √[p₀(1 - p₀) / n]

Substituting values:

z = (0.73 - 0.75) / √[(0.75 × 0.25) / 100]

z = (-0.02) / √(0.001875)

z = (-0.02) / 0.0433

z ≈ -0.460

Answer: z = -0.460