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4.3 Can You Use Either the 95 Percent Conﬁdence
Interval About the Mean OR the One-Group t-test
When Testing Hypotheses?
You are probably asking yourself:
“It sounds like you could use either the 95% conﬁdence interval about the mean or the
onegroup t-test to analyze the results of the types of problems described so far in this topic? Is
this a correct statement?”
The answer is a resounding: “Yes!”
Both the conﬁdence interval about the mean and the one-group t-test are used often in
science research on the types of problems described so far in this topic. Both of these tests
produce the same result and the same conclusion from the data set!
Both of these tests are explained in this topic because some researchers prefer the
conﬁdence interval about the mean test, others prefer the one-group t-test, and still
others prefer to use both tests on the same data to make their results and conclusions
clearer to the reader of their research reports. Since we do not know which of these
tests your researcher prefers, we have explained both of them so that you are
competent in the use of both tests in the analysis of statistical data.
Now, let’s try your Excel skills on the one-group t-test on these three problems at
the end of this chapter.
4.4 End-of-Chapter Practice Problems
1. Suppose that you have been asked to decide if the average petal length of a
particular plant species grown in the state of Missouri has changed from what it
was ﬁve years ago when the average length of this plant in selected sites in
Missouri was 3.10 centimeters (cm). You have been asked to test your Excel
skills on the hypothetical data given in Fig. 4.5 .
(a) Write the null hypothesis and the research hypothesis on your spreadsheet
(b) Use Excel to ﬁnd the sample size, mean, standard deviation, and standard
error of the mean to the right of the data set. Use number format (2 decimal
places) for the mean, standard deviation, and standard error of the mean.
(c) Enter the critical t from the t-table in Appendix E onto your spreadsheet, and
(d) Use Excel to compute the t-value for these data (use 2 decimal places) and
label it on your spreadsheet
(e) Type the result on your spreadsheet, and then type the conclusion in plain
English on your spreadsheet
(f) Save the ﬁle as: PETAL3
2. Suppose that you wanted to study the mass (in grams) of rainbow trout
( Oncorhynchus mykiss ) in a river in southern Colorado in the U.S. Five years
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