MAT 300 M&Ms® Project Part 5 (3 pts) Using the methods in Section 8. 4, test the hypothesis (? = 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. Answer Here n1 = 4179, n2 = 4179, x1 = 588, x2 = 521 Therefore, pred = x1/n1 = 588/4179 = 0. 140703518 Pbrown = x2/n2 = 521/4179 = 0. 124670974 The null hypothesis tested is H0: There is no significant difference in the proportions of red and brown candies. pred = pbrown). The alternative hypothesis is H1: There is significant difference in the proportions of red and brown candies. (pred ? pbrown) The Test Statistic used is [pic] where [pic]= 0. 132687246 Therefore, [pic]= 2. 160335305 Rejection criteria: Reject the null hypothesis, if the observed significance (p-value) is less than the significance level 0. 05. P-value = P ([pic]> 2. 160335305) = 0. 030746722 Conclusion: Reject the null hypothesis, since the observed significance (p-value) is less than the significance level 0. 5. The sample provides enough evidence to support the claim that there is significant difference in the proportions of red and brown candies. Details |Z Test for Differences in Two Proportions | | | | |Data | |Hypothesized Difference |0 | |Level of Significance |0. 5 | |Group 1 | | |Number of Successes |588 | |Sample Size |4179 | |Group 2 | | |Number of Successes |521 | |Sample Size |4179 | | | | |Intermediate Calculations | |Group 1 Proportion |0. 140703518 | |Group 2 Proportion |0. 124670974 | |Difference in Two Proportions |0. 16032544 | |Average Proportion |0. 132687246 | |Z Test Statistic |2. 160335305 | | | | |Two-Tail Test | | |Lower Critical Value |-1. 959963985 | |Upper Critical Value |1. 959963985 | |p-Value |0. 030746722 | |Reject the null hypothesis | |