MAT 300



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 (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. You will need to calculate the weighted p: [pic]

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 ([pic]), 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.

Answer

Let:

pr = population proportion of red candies

pb = population proportion of red candies

The test is :

Ho: pr = pb

Ha: pr ≠ pb

xred = number of red candies, xred = 781

xbrown = number of brown candies , xbrown = 739

n1=n2 = 5842

[pic] = xred /n1 = 781/5842 (sample proportion for red candies)

[pic] = xbrown /n2 = 739/5842 (sample proportion for brown candies)

[pic]=[pic]

Statistic = z = [pic] = [pic]= 1.155

Critical values are: -z(0.025)= -1.96 and z(0.025) = 1.96

Critical Region = {z / z< -1.96 or z> 1.96}

Decision: Since the statistic value (1.155) is not in the reject region we don´t reject Ho

Interpretation: There is no enough evidence to say that proportions are not equal

To confirm the results we run this test using Stat Crunch

Hypothesis test results:

p1 : proportion of successes for population 1

p2 : proportion of successes for population 2

p1 - p2 : difference in proportions

H0 : p1 - p2 = 0

HA : p1 - p2 ≠ 0

Difference |Count1 |Total1 |Count2 |Total2 |Sample Diff. |Std. Err. |Z-Stat |P-value | |p1 - p2 |781 |5842 |739 |5842 |0.0071893185 |0.00622439 |1.1550238 |0.2481 | |

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