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AP Statistics Notes
10.2 Day 1: Tests of Significance
Name_______________________________
Date__________________________
Ex 1: Confidence Intervals on the Graphing Calculator
 A manufacturer of high-resolution video terminals must control the tension on
the mesh of fine wires that lies behind the surface of the viewing screen.
Careful study has shown that when the process is operating properly, the
standard deviation of the tension readings is σ = 43 mV. Here are the tension
readings from an SRS of 20 screens from a single day’s production
269.5
297.0
269.6
283.3
304.8
280.4
233.5
257.4
317.5
327.4
264.7
307.7
310.0
343.3
328.1
342.6
338.8
340.1
374.6
336.1
 Construct a 90% confidence interval using your calculator.
Confidence Intervals vs. Tests of Significance
 You use confidence intervals when you are trying to estimate ______________
_________________________.
 You use ________________________________ when you are trying to assess
the evidence provided by data about some claim concerning a population.
Ex 2: I’m a great free-throw shooter
 Let’s say that I claim I can make 80% of my basketball free-throws.
 You challenge me to make 20 free throws and prove to you that I can shoot
80%.
 I only make 8 out of 20 free throws.
 The probability that I would only make 8 out of 20 free-throws if I really was
an 80% free-throw shooter is 0.0001.
Ex 3: Call the Paramedics!
 Accidents can result in serious injuries to drivers and passengers. Slow
paramedic response time can have serious effects.
 In one city, the mean response time to all accidents last year was μ = 6.7
minutes with a standard deviation of σ = 2 minutes.
 At the end of the following year, the city manger selects a SRS of 400 calls and
examines the response times.
 For this sample, the mean response time was x-bar = 6.48 minutes.
 Does this data provide good evidence that response times have decreased since
last year?
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 If the claim that μ = 6.7 minutes is true, the sampling distribution of x-bar will
be approximately Normal (CLT) with mean
μ = 6.7 minutes and standard
deviation 0.10 minutes.
Null and Alternative Hypotheses
 The statement being tested in a significance test is called the null hypothesis.
(Ho) The significance test is designed to ______________________________
__________________________________________. Usually the null
hypothesis is a statement of “no effect,” or no change from historical values.
 The claim about the population that we are ___________________________
is the alternative hypothesis. (Ha)
What are the hypotheses for the paramedic example?
 What is the null hypothesis?
 What is the alternative hypothesis?
Population vs. Sample
 Hypotheses always refer to some population, not to a particular outcome.
 Be sure to state Ho and Ha in terms of the population, not the sample.
 It doesn’t make sense to state hypotheses about something you already know,
i.e. the sample.
 On the AP exam, you will be penalized if you state the hypothesis using x-bar.
You must state the hypotheses in terms of μ!
One-Sided vs. Two-Sided
 It is not always clear, in particular, whether Ha should be one-sided or twosided.
 If you do not have a specific direction firmly in mind in advance, use a twosided alternative.
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Ex 4: Job Satisfaction
 Does the job satisfaction of assembly workers differ when their work is
machine-paced rather than self-paced?
 One study chose 18 subjects at random from a group of people who assembled
electronic devices.
 Half of the subjects were assigned at random to each of two groups. Both
groups did similar assembly work, but one work setup allowed workers to pace
themselves, and the other featured an assembly line that moved at fixed time
intervals so that the workers were paced by machine.
 After two weeks, all subjects took the Job Diagnosis survey (JDS), a test of job
satisfaction.
 Then they switched work setups, and took the JDS again after two more weeks.
 What type of design is illustrated by this example?
 What is the parameter of interest?
 What is the null hypothesis?
 What is the alternative hypothesis?
Don’t Cheat!
 The alternative hypothesis Ha should express the hopes or suspicions we have
before we see the data.
 It is cheating to first look at the data and then frame Ha to fit what the data
show.
Conditions for Significance Tests
1) SRS from the population of interest
2) Normality
 For means, the population distribution must be normal or the sample
size must be large (n ≥ 30)
 For proportions, the population must be at least ten times larger than
the sample
3) Independent observations
Test Statistics
 A significance test uses data in the form of a test statistic.
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Ex 5: Call the Paramedics!
 Find the test statistic given that Ho: μ = 6.7 minutes,
the estimate of μ is x-bar = 6.48 minutes, and the standard deviation σ = 2
minutes.
 Because the sample result is over two standard deviations below the
hypothesized mean 6.7, it gives good evidence that the response time is
probably less than 6.7 minutes.
P-values
 The probability, computed assuming that Ho is true, that the observed outcome
would take a value as extreme as or more extreme than that actually observed
is called the P-value of the test.
 The smaller the P-value is, the stronger the evidence against Ho provided by
the data.
Ex 6: Call the Paramedics
Ex 7: Calculating a two-sided P-value

Suppose that the z test statistic for a two-sided test is z = 1.7. The two sided pvalue is the probability that Z ≤ -1.7 or Z ≥ 1.7.
Significance Level




Small P-values are evidence against Ho.
How small must a P-value be to persuade us?
There is no fixed rule, but the generally accepted rule is 0.05.
In general, a result with a small P-value, say less than 0.05, is called
statistically significant.
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Statistical Significance
 If the P-value is as small as or smaller than alpha, we say that the data are
statistically significant at a level of α .
 Typically, we will choose 0.05 to represent alpha, thus making a p-value of
0.05 or less statistically significant.
 But, if we decided to make alpha 0.01, a p-value of 0.05 would not be
statistically significant.
(we can decide on a different alpha)
Significance Tests
 To test a claim about an unknown population parameter:
Step 1: Hypotheses
Step 2: Conditions
Step 3: Calculations
Step 4: Sentence
Ex 8: Can you balance your checkbook?
 In a discussion of the education level for the American workforce, someone
says, “The average young person can’t even balance a checkbook.” The
NAEP survey says that a score of 275 or higher on its quantitative test reflects
the skill needed to balance a checkbook. The NAEP random sample of 840
young Americans had a mean score of x-bar = 272, a bit below the checkbookbalancing level. Is this sample result good evidence that the mean for all
young people is less than 275? Assume that σ = 60.
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Step 1: State the Hypotheses
Step 2: Choose the appropriate inference procedure and verify conditions.
 Since σ is known, we will use a one-sample z test for a population mean.
1) The data come from an SRS from the population of interest.
2) The sampling distribution of x-bar is approximately normal (n = 840)
by the CLT.
3) Observations are independent since the entire population of young
adults is more than 10 times larger than the sample.
Step 3: Calculations
Step 4: Interpret your results in context.
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