This assignment continues the candy data study by applying some statistical tests. For sample
sizes and degrees of freedom, think carefully about what you are testing and comparing: are they
years, candies, packages, colours, or something else? For each statistical test, clearly state what
was or was not statistically significant.
First, compare the distributions of the weight of candy per package in the old and new processes.
1. Draw 2 histograms by hand or using software. In the first histogram show the distribution of
the weight of candy per pack in the old process. In the second histogram show the weight
distribution for the new process. Use the same vertical and horizontal scales for both
diagrams so that they can easily be compared. You might need to try several “bin limits” to see
what makes both distributions easiest to see. In about 2 sentences, describe the main similarities
or differences you can see in the 2 histograms.
2. Perform a statistical test to compare the “width” of the 2 distributions. That is, do a 2-sample
F-test to compare the variance of the old process to that of the new one. Make sure the Fcalculated value is greater than 1. You can perform this test using software or by hand. For
hand calculations you can use the Excel functions “finv()” or “f.inv()” to get the critical value
and “fdist()” or “1-f.dist()” to get the significance p. In about 1-2 sentences, briefly describe what
the test indicates.
3. Perform 3 statistical tests of means as follows. After each one, briefly describe what the test
indicates in about 1-2 sentences.
(a) Do a 2-sample t-test assuming unequal variances to compare the mean of the old process to
the mean of the new one. Use software for this calculation.
(b) Do a 1-sample t-test to compare the old process mean to the label weight. Do this calculation
by hand. You can use the Excel functions “tinv()” or “t.inv.2t()” to get the critical value and
“tdist()” or “t.dist.2t()” to get the p.
(c) Do a 1-sample t-test by hand to compare the new process mean to the label weight.
Next, examine the share of orange candies as follows.
4. Given that there are 5 colors of candies, one would expect to find about 20% of them are of
each color. Investigate whether this was the case for the old process by performing a statistical
test to compare the actual proportion of orange candies to the expected proportion. Perform the
same test for the new process. What do these 2 test results indicate?
Finally, summarize your findings as follows.
5. How does the new process compare to the old process? In what ways was the new process
better, and in what ways was the old one better? Your answer should take about 2-4 sentences.
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