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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