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This project will cover topics from Chapter 1 up through Chapter 8 of your textbook. All
papers will need to be submitted on Ivy Learn. You will be turning in a paper that should
include section headings, drawing/graphics and tables when appropriate and complete
sentences which explain all analysis that was done in addition to all conclusions and results.
All work should be your own. Plagiarism will result in a project score of 0.
You will be performing an analysis on Iris setosa (wildflower) and their petal lengths. You
will need to know that research has shown that the petal length of Iris setosa is
approximately normal and has a mean of 𝜇 = 1.5 𝑐𝑚 and a standard deviation of 𝜎 = 0.2 𝑐𝑚
.
The following sample was collected by Dr. Edgar Anderson, who studied these flowers
extensively.
Here is the sample data collected from the Gaspe Peninsula, Quebec: (I have also included a
file with this information in the project folder for use in uploading to Cengage SALT or
Excel)
Petal Length in Centimeters for Iris Setosa
1.4 1.4 1.3 1.5 1.4
1.7 1.4 1.5 1.4 1.5
1.5 1.6 1.4 1.1 1.2
1.5 1.3 1.4 1.7 1.5
1.7 1.5 1.0 1.7 1.9
1.6 1.6 1.5 1.4 1.6
1.6 1.5 1.5 1.4 1.5
1.2 1.3 1.4 1.3 1.5
1.3 1.3 1.3 1.6 1.9
1.4 1.6 1.4 1.5 1.4
Project Guidelines:
1. Descriptive Statistics/Graphs:
a. Calculate some descriptive statistics for variable, x, the petal length of Iris
setosa from the Gaspe Peninsula. These should include (but not limited to)
the mean, median and standard deviation. Organize these values neatly in a
table with labels and then write a paragraph describing your statistics.
Round any decimals to two decimal places. (You can use SALT to come up
with the descriptive statistics)
b. Create a histogram of the variable, x, the petal length of Iris setosa. Use the
histogram to identify the shape of the distribution. (This can easily be
accomplished by uploading the data into Cengage SALT and setting the
bin/class width for 0.1 and adjusting the starting point to an appropriate
value). Include the histogram image in your paper as long as your discussion
on the shape of the distribution.
2. Normal Distribution application:
a. A friend of yours spotted some of the Iris setosa flowers while on a nature
hike and measured petal lengths from three of the flowers. The
measurements that they calculated were 1.8 cm (Flower A), 1.4 cm (Flower
B), and 0.7 cm (Flower C). Calculate z-scores for each of the reported flower
petal measurements (using population mean and standard deviation stated
in project intro) and provide interpretations for the z-scores (after looking
up probabilities on the table). Include your formulas in your paper. You also
need to include interpretations that indicate how “rare” your observations
are in the body of your paper. (Format: Flower A with a petal length of ______
had a corresponding z-score of _____. This means that _______% of Iris setosa
petal lengths are longer/shorter than it’s petal length. This value is/is not a
rare observation because _________.)
3. Confidence Interval applications:
a. Using the sample data of 50 petal lengths from the Gaspe Peninsula,
compute a 99% confidence interval for the population mean petal length of
all Iris setosas. Interpret the confidence interval in words. Round interval
values to two decimal places. Write a summary of how you calculated this
including the formula.
b. How many more Iris setosas petal lengths would we need to include in our
sample if we want to be 99% confident that the sample mean is within a
maximal margin of error of 0.04 cm of the population mean petal length?
Write a summary of how you calculated this including the formula.
4. Hypothesis Testing applications:
a. A botanist in Alaska is concerned that climate change is affecting the growth
of Iris wildflowers in Alaska. He collected a sample of 35 Iris setosa petal
lengths that had a mean of 𝑥 = 1.56 𝑐𝑚 and standard deviation of s = 0.23
cm. For this test, you may use the fact that previous studies show the
distribution of petal lengths of Iris setosa are approximately normal and that
the population standard deviation is known to be 0.2 cm. Do the data
indicate that the mean petal length of the Iris setosa in Alaska is greater than
1.5 𝑐𝑚? Use 𝛼 = 0.01. You will need to state your null and alternate
hypothesis, describe which distribution we will use and calculate the
appropriate test statistic. Then state the p-value and conclusion for the test.
Interpret your results.
b. Considering the sample of 50 petal lengths from the Gaspe Peninsula (intro)
and the sample of 35 petal lengths from the botanist in Alaska, do the data
indicate that the petal lengths of the Iris Setosa in Alaska are different (either
way) than the petal lengths of the Iris Setosa in the Gaspe Peninsula? Assume
the distribution of petal lengths in both areas is approximately normal. Use a
5% level of significance. (For this part, assume we do not know anything
about the population standard deviations for each specific area and base
your test only on the sample means for each area and the sample standard
deviations – You will have to reference earlier steps in the project for the
sample means and standard deviations.) You will need to state your null and
alternate hypothesis, describe which distribution we will use and calculate
the appropriate test statistics. Then state the critical value and use the
critical region test to reach a conclusion. Interpret your results.
5. Put everything together into an organized paper and submit on IvyLearn.
Graded Item Points
Possible
Points
Earned
Organization/Formatting
Paper is well organized with clear section headings, well organized
information and graphics when appropriate 10
Descriptive Statistics/Graphs
Statistics organized in table with labels/Paragraph written discussing
descriptive statistics 10
Histogram graphic included and description of the shape of the distribution 10
Normal Distribution
Z-scores were calculated for three flowers provided, formulas included.
Appropriate interpretation of z-scores were included 15
Confidence Interval
Calculations for the 99% confidence interval included as well as interpretation 15
Calculations of finding the sample size needed to be within a certain margin of
error 10
Hypothesis Testing
Hypothesis test 1: Included null and alternate hypothesis statements,
discussion of distribution to use, test statistic calculations, p-value and
conclusion and interpretation
15
Hypothesis test 2: Included null and alternate hypothesis statements,
discussion of distribution to use, test statistic calculations, critical value and
conclusion and interpretation
15