# Math 300 M & M project Part 5

**Question description**

MAT 300

M&Ms® Project

Part 5 (3 pts)

Using the methods in Section 8.4, test the hypothesis (α =
0.05) that the population proportions of red and brown are equal (p_{red}
= p_{brown}). You are testing if
their proportions are equal to one another, NOT if they are equal to one
another AND equal to 13%. NOTE: These are NOT independent samples, but we
will use this approach anyway to practice the method. This also means that n_{1} and n_{2}
will both be the total number of *candies*
in all the bags. The “x” values for red
and brown are the counts of each we found on the Data page. You will need to calculate the weighted
p:

Red, x = 581 and Brown, x = 557

Be sure to state clear hypotheses, test statistic, critical value or p-value, decision (reject/fail to reject), and conclusion in English. Submit your answer as a Word, Excel, .rtf or .pdf format through the M&M® project link in the weekly course content.

HELP

You can use StatCrunch or the TI to help with this test. Needed information for both tools include:

x1 = number of red

n1 = total number of candies

x2 = number of brown

n2 = total number of candies

For the TI, you will want 2-PropZTest. Then select the appropriate alternative (not equal), and Calculate then enter. The output will have the test statistic (z), p-value (p), sample p values, weighted p (), then repeat of sample sizes.

For StatCrunch, you will select Stat > Proportions > Two Sample > with summary. The output will contain the test statistic (Z-Stat) and p-value.

Additional help is available in the Online Math Workshop under MAT300 Archived Workshop. Specifically Two Sample Inferences and Using Technology – Two Sample.

At the end of this project, you will be writing a report, explaining the method and presenting the results from each part of the project. You might find it useful to write this as you complete the work, so the report will be mostly written by the time it is assigned.

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