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Chapter 12 Significance Tests in Practice
One sample mean and proportion hypothesis tests
Skittle Quick Lab:
It has been advertised that the color distribution for the original Skittles is 20% for each of the five colors.
Since we have only developed tests for one sample statistics, lets test the company's claim of 20% for the green
skittles.
Ho:
Ha :
α=
Conditions:
Test Statistic:
P-value =
Conclusion:
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Conducting Different Hypothesis Tests
The structure of every hypothesis test will always be the same. What changes from test to test is the statistic and parameter
that we will be using. The following are the different types of hypothesis tests that you will encounter:
One-sample t test (mean)
One-sample proportion test
Two-sample mean test
Two - sample proportion test
χ2 Goodness of fit
χ2 Test of Independence
Linear Regression t- test (slope)
Ex: Sweet cola
Diet colas use artificial sweeteners to avoid sugar. These sweeteners gradually lose their sweetness over time. Manufacturers
therefore test new colas for loss of sweetness before marketing them. Trained tasters sip the cola along with drinks of standard
sweetness and score the cola on a "sweetness scale" of 1 to 10. The cola is then stored for a month at high temperature to imitate
the effect of four months' storage at room temperature. Each taster scores the cola again after storage. Our data are the
differences (score before storage minus score after storage) in the tasters' scores. The bigger these differences, the bigger the
loss of sweetness. Here are the sweetness losses for a new cola, as measured by 10 trained tasters:
2.0
0.4
0.7
-0.4
2.2
-1.3
1.2
1.1
Are these data good evidence that the cola lost sweetness in storage?
2.3
2.0
chapter 12 notes 08­09.notebook
March 30, 2012
chapter 12 notes 08­09.notebook
March 30, 2012
Ex. 2: Diversify or be sued!!!
An investor with a stock portfolio worth several hundred thousand dollars sued his broker because
lack of diversification in his portfolio let to poor performance (low returns). The table below gives
the rates of return for the 37
39 months that the account was managed by the broker. An arbitration
panel compared these returns with average of the Standard & Poor's 500 stock index for the same
period. Consider the 37
39 monthly returns as a random sample from the monthly returns the broker
would generate if he managed the account forever. Are these returns compatible with a population
mean of 0.95%, the S&P average?
Monthly rates of return on a portfolio (%)
-8.36
-2.35
-9.16
1.28
5.04
4.33
1.63
-3.58
-1.25
-0.65
-7.24
2.35
-2.27
6.13
-1.22
4.34
-2.14
-2.93
7.00
-10.27
12.22
-1.01
-9.14
-15.25
-5.11
-7.21
-1.41
-2.64
-8.66
-0.80
-0.09
12.03
Construct a 95% confidence interval for the above problem. Does your interval support your conclusion?
PAIRED T-TEST
This test is processed just like a one sample mean test because we only have one set of data that we
are using. The sweetness of cola example is a paired test. It is paired by taster.
Ex. Floral scents and learning
6.82
-1.03
-1.44
7.34
-2.56
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Ex. 1
March 30, 2012
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March 30, 2012
Confidence Intervals and Hypothesis Tests for Proportions:
Ex.: Work Stress
According to the National Institute for Occupational Safety and Health, job stress poses a major
threat to the health of workers. A national survey of restaurant employees found that 75% said
that work stress had a negative impact on their personal lives. A random sample of 100 employees
from a large restaurant chain finds that 68 answer "Yes" when asked, "Does work stress have a
negative impact on your personal life?" Is this good reason to think that the proportion of all
employees in this chain who would say "Yes" differs from the national proportion?
Construct a 95% CI for this situation.
This is important!!!!! In the z-test when we are doing the standard deviation we use p, but in
the confidence interval we use p-hat for the standard error.
chapter 12 notes 08­09.notebook
March 30, 2012
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