Question

A new bus route has been established between downtown Denver and Englewood (a suburb of Denver). Eric has taken the bus to work for many years. For the old bus route, he knows from long experience that the mean waiting time between buses at his stop was 20 minutes.
However, a random sample of 34 waiting times between buses using the new route had a mean of 17.2 minutes with a sample standard deviation of 6.4 minutes.

Does this indicate that the population mean waiting time for the new route is shorter than what it used to be? Use a significance level of α = 0.01.

Step 1: State the null and alternate hypotheses.

What is the initial assumption?

We ALWAYS assume ____________________ is true.
We categorize this test as a ______ (circle one: left-tailed, right-tailed, or two-tailed) test.

Step 2: the level of significance is _________
Shade the level of significance in the graph below.

Step 3: Check conditions to choose the correct test.

The correct test to test these hypotheses is a ______. Why? (a) Z test
(b) T Test

(c) Not enough information given. Do not test

Step 4: Use your calculator to find the test statistics and the p-value.

The test statistics is ____________
The p-value is ____________ Shade the p-value in the graph in Step 2.

Step 5: Make your decision about H0.
(Decide if you still believe in the truth of the initial assumption (H0 is true) by comparing the p-value with the level of significance ?).

Based on the p-value, you decide to ___________ at a level of significance of 0.01. (a) accept H0
(b) reject H0
(c) fail to reject H0

(d) Cannot determine normality; do not conduct the test.
This means that we _____________ (Circle one: no longer or still) believe in the truth of the initial

assumption H0.

Step 6: State your conclusion about Ha.

Answer 1

Step 1: State the null and alternate hypotheses.

We ALWAYS assume null hypothesis is true.
We categorize this test as a left-tailed test.

Ho : µ = 20
H1 : µ < 20

Step 2: the level of significance is 0.01.

Step 3: The correct test to test these hypotheses is a T-Test.

Step 4: x̅ =   17.2, s =   6.4, n =   34

Test statistics:

t = (x̅- µ)/(s/√n) = -2.551

df = 34-1 = 33

p-value = T.DIST(-2.551, 33, 1 ) = 0.0078

Step 5: Decision:

Based on the p-value, you decide to Reject Ho at a level of significance of 0.01.

This means that we no longer believe in the truth of the initial assumption H0.

Step 6: Conclusion:

There is enough evidence to conclude that the population mean waiting time for the new route is shorter than what it used to be, at 0.01 significance level.