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 value of the calculated test statistic?
A)Z = 6.416
B)Z = 3.208
C)Z = -3.208
D)Z = -6.416
E)Z = 1.833

Question

Quizplus · Accepted Answer

The calculated test statistic for a hypothesis test of a single proportion is calculated using the formula:

Z = (p̂ - p) / (sqrt(p * (1-p) / n))

where p̂ is the sample proportion, p is the hypothesized population proportion, and n is the sample size.

In this case, the hypothesized population proportion is 0.18 (since historical data shows that 18% of airplanes have arrived late) and the sample size is 1240, with 310 late arrivals.

Calculating the sample proportion:

p̂ = 310 / 1240 = 0.25

Plugging in the values:

Z = (0.25 - 0.18) / (sqrt(0.18 * (1 - 0.18) / 1240))

Z = 6.416

Therefore, the value of the calculated test statistic is Z = 6.416.

The correct answer is A).

A Major Airline Company Is Concerned That Its Proportion of Late