# Stat2040 Lec

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22 Sep 2014
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Supporting Videos For This Chapter
8msl videos (these are also given at appropriate places in this chapter):
An Introduction to Hypothesis Testing (9:54) (http://youtu.be/tTeMYuS87oU)
ZTests for One Mean: Introduction (11:13) (http://youtu.be/pGv13jvnjKc)
ZTests for One Mean: The Rejection Region Approach (10:24) (http://youtu.be/60x86lYtWI4)
ZTests for One Mean: The p-value (10:02) (http://youtu.be/m6sGjWz2CPg)
ZTests for One Mean: An Example (6:26) (http://youtu.be/Xi33dGcZCA0)
What is a p-value? (Updated and Extended Version) (10:51) (http://youtu.be/UsU-
O2Z1rAs)
Type I Errors, Type II Errors, and the Power of the Test (8:11) (http://youtu.be/7mE-
K_w1v90)
Calculating Power and the Probability of a Type II Error (An Example) (11:32)
(http://youtu.be/BJZpx7Mdde4)
What Factors Aﬀect the Power of a Z Test? (12:25) (http://youtu.be/K6tado8Xcug)
Statistical Signiﬁcance versus Practical Signiﬁcance (4:47) (http://youtu.be/_k1MQTUCXmU)
The Relationship Between Conﬁdence Intervals and Hypothesis Tests (5:36)
(http://youtu.be/k1at8VukIbw)
t Tests for One Mean: Introduction (13:46) (http://youtu.be/T9nI6vhTU1Y)
t Tests for One Mean: An Example (9:43) (http://youtu.be/kQ4xcx6N0o4)
Assumptions of the t Test for One Mean (7:54) (http://youtu.be/U1O4ZFKKD1k)
Other supporting videos for this chapter (not given elsewhere in this chapter):
One-Sided Test or Two-Sided Test? (9:25) (http://youtu.be/VP1bhopNP74)
Hypothesis Testing in 17 Seconds (0:17) (http://youtu.be/wyTwHmxs4ug)
Hypothesis tests on one mean: t test or z test? (6:58)
Using the tTable to Find the P-value in One-Sample tTests (7:11)
(http://youtu.be/tI6mdx3s0zk)
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Hypothesis Testing
In hypothesis testing we translate a question of interest into a hypothesis about the value
of a parameter, then carry out a statistical test of that hypothesis.
Examples of questions that hypothesis testing may help to answer:
Do more than half the adults in a certain area favour legalization of marijuana?
Is the mean highway fuel consumption of a new model of car diﬀerent from what the
manufacturer claims?
Example 0.1 Do Cairo traﬃc oﬃcers tend to have greater lead levels in their blood than
oﬃcers from the suburbs?
Boxplots of lead levels of 126 Cairo traﬃc oﬃcers and 50 oﬃcers from the suburbs:
10
20
30
40
Cairo Traffic Suburbs
Figure 1: Lead levels in the blood of Egyptian police oﬃcers.
The boxplots seem to show that Cairo oﬃcers tend to have a higher blood lead level con-
centration. But is this a statistically signiﬁcant diﬀerence?
After formulating the research question of interest, we will turn it into appropriate null and
alternative hypotheses:
The alternative hypothesis, denoted by Ha, is often the hypothesis the researcher
is hoping to show. (The alternative hypothesis is sometimes referred to as the research
hypothesis.)
The null hypothesis, denoted by H0, is the hypothesis of no eﬀect or no diﬀerence.
(The null hypothesis is sometimes referred to as the status quo hypothesis.)
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Suppose we wish to investigate whether males and females have diﬀerent variability in their
scores on the SAT exam. The appropriate hypotheses would be:
Example 0.2 A mining company has been ordered to reduce the mean arsenic level in the
soil on one of its properties to no more than 100 ppm.
Suppose an environmental organization strongly suspects that the mining company has not
complied with the order. If the burden of proof is on the environmental organization to
show that the mining company has not complied, then the mining company would be given
the beneﬁt of the doubt in the hypotheses:
Now suppose the situation was changed slightly, and the burden of proof was on the mining
company to show that there is less than 100 ppm of arsenic on average. They may wish to
test:
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