Introduction To Statistics And Data Analysis 5th Edition By Peck – Test Bank

Chapter 11: Comparing Two Populations or
Treatments
Section 11.1
Name ___________________________
1. Comparison of means focuses on the difference between two population or treatment
means, . When testing the hypothesis, , there are three
possible alternative hypotheses.
m m 1 – 2 0 1 2 : Hm m o – =
a) Using correct statistical notation, list these three alternative hypotheses.
b) For each alternative hypothesis in part (a), give an example of a situation from your
own experience or your reading where one might use that alternative hypothesis. Be
sure to clearly specify a context, define your variables, and state the null and
alternative hypothesis.
Chapter 11, Quiz 1, Form A
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2. When testing hypotheses about and constructing confidence intervals for , we
utilize the statistic,
m m 1 – 2
1 2 x – x . What are the mean and variance of the sampling
distribution of 1 2 x – x ?
3. When comparing two population means, it is important to make the distinction
between independent samples and paired samples. What makes two samples
independent?
Chapter 11, Quiz 1, Form A
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Downy Woodpecker
Bill Lengths (cm)
Male Female
2.01 1.78
1.84 1.76
1.86 1.74
1.91 1.82
1.75 1.87
1.79 1.84
1.88 1.82
2.05 1.87
1.85 1.93
1.90 1.76
1.94 1.96
1.86 1.86
4. Researchers have hypothesized that female Downy Woodpeckers
avoid the feeding areas of socially dominant males; that is, the
males chase them away from prime spots. An alternative
opinion is that there are important physical characteristics of
males and females that might lead them to choose different
foraging locations. One such characteristic could be the bill
length of the males and females; it may be that longer bills let
one gender or the other drill deeper into a tree and thus get more
food per tree.
The data in the table at right are the bill lengths of 12 male and
12 female randomly selected Downy Woodpeckers caught and
released in a banding survey. The investigators would like to
know whether these data provide evidence that the males and
females differ in bill size.
a) Using a graphical display of your choosing, assess the plausibility of the assumption
that the distributions of bill lengths are approximately normal. State your conclusion
in a few sentences.
Chapter 11, Quiz 1, Form A
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b) Assuming that it is OK to proceed with a two-sample t procedure, determine if there
is sufficient evidence to conclude that there is a difference in mean bill length for
males and females.
c) In a few sentences, state any concerns you have about your conclusions in part (b),
based on your results from part (a). If you have no concerns, write “No concerns.”