Homework Questions?
Section 9.3
Tests about a Population Mean
One Sample t Test
𝑥−𝜇0

𝑡=

Find the p-value by calculating the probability of getting a
t statistic this large or larger in the direction specified by
the alternative hypothesis with 𝑑𝑓 = 𝑛 − 1
𝑠𝑥
𝑛
Computing the test statistic and p-value of
AAA batteries from section 9.1

The battery company wants to test 𝐻0 : 𝜇 = 30 vs.
𝐻𝑎 : 𝜇 > 30 based on a SRS of 15 new AAA batteries
with a mean lifetime of 𝑥 = 33.9 hours and standard
deviation 𝑠𝑥 = 9.8 hours. What is the test statistic? (t)

Find the p-value.

Can we still make conclusions?
Two-Sided Tests

What if you were performing a test of 𝐻0 : 𝜇 = 5 vs.
𝐻𝑎 : 𝜇 ≠ 5 based on a sample of 𝑛 = 37 and obtained
𝑡 = −3.17?
Example – Health Streams


The level of dissolved oxygen (DO) in a stream or river is
an important indicator of the water’s ability to support
aquatic life. A researcher measures the DO level at 15
randomly chosen locations along a stream. Here are the
results in mg/l:
4.53
5.04
3.29
5.23
4.13
5.50
4.83
4.40
5.42
6.38
4.01
4.66
2.87
5.73
5.55
XX
A DO level below 5 mg/l puts aquatic life at risk.
Healthy Streams

Can we conclude that aquatic life in this stream is at risk?
Carry out a test at the 𝛼 = 0.05 significance level to help
you answer the question.
State:

Plan:

Healthy Streams

Do:

Conclude:
Healthy Streams

Given your conclusion, which kind of mistake – Type I or
Type II error – could you have made? Explain what this
would mean in context.
Again…look at a confidence interval…

Look at 95% confidence interval…

∗ 𝑠𝑥
±𝑡
𝑛
For means: 𝑥
Paired Data - Flip to page 581


Matched Pairs!
Only do (3, 4, 5)
Homework
Pg. 587 (63-69 odd, 70, 73-79 odd, 91, 95, 96, 99-104)