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, 260 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 using the following hypotheses H 0 and H 3 :p>0.18

Step 1: What is the value of the test statistic? Round your answer to four decimal places

Step 2: What is the p-value of your test? Round your answer to four decimal places

Step 3: What is the conclusion of this problem?

Answer 1

Answer)

Null hypothesis Ho : p = 0.18

Alternate hypothesis Ha : P > 0.18

N = 1240

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 223.2

N*(1-p) = 1016.8

Both the conditions are met so we can use standard normal z table to estimate the P-Value

Test statistics z = (oberved p - claimed p)/standard error

Standard error = √{claimed p*(1-claimed p)/√n

Observed P = 260/1240

Claimed P = 0.18

N = 1240

After substitution,

Test statistics z = 2.72

From z table, P(z>2.72) = 0.0033

P-value = 0.0033

As the p-value is small we reject the null hypothesis Ho.

We have enough evidence to conclude that p > 0.18.