Question

A major airline company is concerned that its proportion of late arrivals has substantially increased in the past month. Historical data shows that on the average 18% of the company airplanes have arrived late. In a random sample of 1,240 airplanes, 310 airplanes have arrived late. If we are conducting a hypothesis test of a single proportion to determine if the proportion of late arrivals has increased, what is the correct statement of null and alternative hypotheses

Answer 1

The correct statement is

The null hypothesis is
`H_o : p = 0.18`

The alternative hypothesis is
`H_a : p > 0.18`

Explanation:

From the question we are told that

The population proportion is p = 0.18

The sample size is n = 1240 airplane

The number of airplane is k = 310

Generally the sample proportion is

`\^ p = (k)/(n)`

=>
`\^ p = (310)/(1240)`

=>
`\^ p =0.25`

The null hypothesis is
`H_o : p = 0.18`

The alternative hypothesis is
`H_a : p > 0.18`