Name:
Friday T.A. name/Class time:
Monday/Wednesday lecturer:
September 30, 2011
Lab 5: Chapter 6
READ THIS: In the material for the first exam, especially Sections 3.3 and 5.2, you
learned about the difference between a population and a sample. There is a parameter for
the whole population (for example the average age for all U.S. residents), but it would be
too difficult, time-consuming, and expensive for us to get the number directly through a
census. Instead, we usually choose to take a random sample and calculate a statistic as an
estimate for the population parameter. However, we also know that every time we take a
random sample from the population, we will get a different sample statistic simply due to
random variability. When we use a statistical technique called inference, we are taking
into account random variability when we estimate the population parameter from the
sample statistic. Confidence intervals and hypothesis testing are types of inference.
1. (3 points) Using the diagram below, fill in the blanks with these terms: inference,
sampling, , σ, s, x .
population
sample
Confidence Intervals
Using Internet Explorer, go to the website for your textbook:
www.whfreeman.com/ips6e. Click on “statistical applets” and then on “confidence
interval.” Read the explanation at the top of the webpage. Use the 95% confidence level
until you are told to change.
2. (0.5 points) What does the  stand for? ___________________________
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3. (0.5 points) When we calculate a confidence interval in real-life (non-applet)
circumstances, do we know what  is? Circle your answer: Yes No
Press the “sample” button to create a single confidence interval. Did your confidence
interval from your single sample include the true population mean?
4. (1 point) What does the red slash in the middle of the confidence interval represent?
(Answer with a symbol and in words.)
Try creating some more confidence intervals by hitting the “sample” button several more
times. Check to see if all of your confidence intervals include the true population mean.
If you create 100 confidence intervals, what percentage of your confidence intervals do
contain the true population mean?
Try changing the confidence level and observe the results to your intervals.
5. (0.5 points) As the confidence level increases, the width of the interval (circle one):
increases / decreases / stays the same
6. (0.5 points) As the confidence level increases, the percentage of intervals which
contain the true population mean (circle one):
increases / decreases / stays the same
This applet doesn’t let us adjust the sample size for our individual simple random
samples. The formula for the confidence interval for the population mean when the
population standard deviation is known is:
x  z*

n
7. (0.5 points) As the sample size increases, the width of the interval (circle one):
increases / decreases / stays the same.
8. (0.5 points) As the sample size increases, the center of the interval generally (circle
one):
moves right / moves left / stays the same.
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Hypothesis testing
READ THIS: For hypothesis testing, we don’t know the true population mean, but we do
have a reasonable guess, possibly from previous research, which we call 0. This number
goes in the null hypothesis. The point of hypothesis testing is to see how the true
population mean compares to this reasonable guess without having to take a full census.
Since we don’t know what the population mean really is, we use a simple random sample
and calculate a sample statistic. However, we know that every time we take a sample,
there is always random variability, so we need to take that into account when we estimate
our population parameter. This is why you don’t just compare the sample statistic
directly to 0. Instead, we need to see how unusual our sample statistic is if the null
hypothesis is true. If the sample statistic isn’t too many standard deviations away from
0, then random chance could explain any discrepancy, and we have no reason to reject
the null hypothesis. If the sample statistic is very far away from 0, then we say that our
results are just too weird to have occurred simply due to random variation alone, and
there is something wrong with our null hypothesis. How weird is too weird? We use a
cut-off point, called the significance level (, usually 0.05). If the P-value is less than the
significance level, meaning results as weird as yours have a very small probability of
occurring due to random chance, you reject the null hypothesis.
9. (4 points) Fill in the chart below for how we make decisions about conclusions to
hypothesis tests. Your answer choices are in boldface type.
P-value > 
a) Is the sample mean x near or far from the
reasonable guess for the population mean 0?
b) On the Normal curve diagram for this
hypothesis test, does the P-value take up a small
or big area?
c) Conclusion to the hypothesis test:
Reject H0,
Do not reject H0, or
Accept H0
d) There is or is not evidence in favor of the
alternative hypothesis.
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P-value  
The mean weight for a simple random sample of 12 Hostess Twinkie snack cake packs is
found to be 15.96 oz. The overall population standard deviation of a pack of Hostess
Twinkies is 0.15 oz. The package promises a weight of 16 oz. Is the true population
mean weight of a Twinkie package different from 16 oz? Use a 5% significance level.
10. (6 points) For the story above, state the hypotheses, calculate the test statistic and
P-value (using the Normal table from the course webpage or your book), and state
your conclusion in terms of the story. Be sure to state whether your conclusion
refers to the population or the sample.
11. (1.5 points) Neatly label the Normal curve below with the number and symbol for
the mean you use in your null hypothesis (0) and the sample mean ( x ). Also shade
and label the appropriate part of the curve which shows the P-value.
12. (1.5 points) Neatly label the Normal curve below with the number and symbol for
z = 0, and the test statistic (z0). Also shade and label the appropriate part of the curve
which shows the P-value.
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