# Hypothesis Testing Exercise

M&Ms® Project

Part 5

Test the hypothesis (α = 0.05) that the population proportions of red and brown are equal (pred = pbrown). 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 n1 and n2 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. We will need to calculate the weighted p:

State clear hypotheses, test statistic, critical value or p-value, decision (reject/fail to reject), and conclusion in English.

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

At the end of this project, we will be writing a report, explaining the method and presenting the results from each part of the project.

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#### Solution Summary

The solution guides you to perform the hypothesis testing step by step. Finally, a conclusion is made based on the test result.