Question

On Time Airlines claims their average delay is less than 15 minutes per flight. A random sample of 35 flights has a sample mean of 14 minutes and standard deviation of 7 minutes. You will need to test the claim that the average delay is less than 15 minutes per flight using a 2.5% level of significance.

a) State the hypotheses

b) Find the rejection region.

c) Will you reject or retain the null hypothesis? Show all work to support your answer.

d) What is the p-value for this sample of flights?

e) If it turns out the true mean value is 14 minutes, have you committed an error, and if so, what type of error?

Answer 1

Solution:

Part a

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: the average delay is 15 minutes per flight.

Alternative hypothesis: the average delay is less than 15 minutes per flight.

H0: µ = 15 versus Ha: µ < 15

This is a lower tailed test.

Part b

We are given

n = 35

df = n – 1 = 34

α = 0.025

Critical value = -2.0322

(by using t-table or excel)

Reject H0 when t < -2.0322

Part c

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 15

Xbar = 14

S = 7

n = 35

t = (Xbar - µ)/[S/sqrt(n)]

t = (14 – 15)/[7/sqrt(35)]

t = -0.8452

We do not reject H0 because test statistic t is not less than critical value of -2.0322.

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the average delay is less than 15 minutes per flight.

Part d

P-value = 0.2020

(by using z-table)

Part e

Answer: Type II error

(because we do not reject the null hypothesis)