Example 4 A random sample of students on a college PENHIES NICKELS DIME '1"an campus was asked to count the number of pennies, nickels, dimes, and quarters they had on their person. The summary information is shown in the table to the right. Note: We can consider each of the four data sets as samples from their respective populations of pennies, nickels, dimes, and quarters. LulIM'U'IG'INLU-b 3 5 B E 4 3 2 3 5 {a} First, verify the requirements that must be satisfied to use the one-way AN OVA procedure and complete the table: El Each sample 5R5 Normal probability plots Show El Samples independent of each other significant linear correlation D Samples EUITIE {mm "DIME\"? distributEd populations and buxp'ats revea' no out'iers_ El Populations have equal variances Category: 11; Sample Means Sample Standard Deviations Pennies Sir S 231? lib] At the it = .05 level of significance, test whether the population means for the various coinage is different. STEP 1 Write the null and alternative hypotheses. STEP 2 State the value of a: n1 (:1 s)2+ nzz E)2+---+nk{3_ckE}2 STEP 3 Compute the tESt Statistic: F = m nk Using Technology, verify your results by running an ANOVA Test: Fo = pvalue = Factor Error df = of = = 55 = M5 = M5 = STEP 5 State conclusion: {1:} Sketch boxplots of the four sets of data: [In the plots support the results obtained in part [b]