3. An environmentalist wanted to determine if the mean acidity of rain differed among Alaska, Florida, and Texas. He randomly selected six rain dates at each of the three locations and measured the pH level. He obtained the following data Alaska Florida Texas 5.41 4.87 5.46 5.39 5.18 6.29 4.90 4.40 5.57 5.14 5.12 5.15 4.80 1.89 5.45 5.24 5.06 5.30 Source: National Atmospheric Deposition Program. (a) An agricultural researcher wants to know if the mean pls in the rainwater are the same. State the null and alternative hypotheses. (Points: 2) . HO: The pH is the rain water is equal in all states . HI: The pH is the rain water is not equal in one or more states (b) State the requirements that must be satisfied to use the one-way ANOVA procedures. (Points: 2) . There has to be more than two samples . The samples have to be independent . The samples are drawn from a normally distributed population . Each sample has a common variance (c) Use Microsoft Excel to test the hypothesis that the mean pis in the rainwater are the same at the a = 0.05 level of significance. Copy and paste into your Word document the 12worksheet ply containing the Microsoft Excel results from the hypothesis test. (Points: 3.34) Anova: Single Factor SUMMARY Groups Count Sum Average Variance Alaska 30.88 5.14666667 0.06366667 Florida 29.52 4.92 0.0802 Texas 33.22 5.53666667 0.15750667 ANOVA Source of of MS F P-value F crit Variation Between 1.16751111 2 0.58375556 5.8109543 0.01353289 3.68232034 Groups Within Groups 1.50686667 15 0.10045778 Total 2.67437778 17 (d) State the correct conclusion at the a = 0.05 significance level ("There is sufficient evidence at the a = 0.05 significance level to support..." or "There is NOT sufficient evidence at the a = 0.05 significance level to support..."). (Points: 2) Reject HO (e) Use Microsoft Excel to draw one boxplot of the pl in rain for each of the three states. Format the horizontal axis of each boxplot with the same minimum, maximum, major unit, and minor unit so that the three boxplots can be easily compared. Copy and paste the three boxplots into your Word document. (Points: 6) 13\fTexas Ch 4 (f) Do the boxplots from part (e) support the results from part (d)? Explain. (Points: 2) . Yes, Texas continues to show how it is different from the other three. (g) Use Tukey's test to determine which pairwise means are significantly different using a familywise error rate of a = 0.05 (i) State the null and alternative hypotheses for each pair. Make sure you state the null and alternative hypotheses for the smaller and the larger sample mean for each pair. (Points: 2) . HO: There is no significant difference in pl for Texas and Alaska, us - u1 = 0 . H1: There is significant difference in pl for Texas and Alaska, us - un # 0 . HO: There is no significant difference in pH for Texas and Florida, us - uz = 0 . HI: There is significant difference in pH for Texas and Alaska, u3 - uz # 0 . HO: There is no significant difference in pH for Alaska and Florida, un - 2 = 0 . HI: There is significant difference in pH for Alaska and Florida, un - uz # 0 15(ii) Compute the test statistic for each pairwise difference. Make sure you subtract the smaller sample mean from the larger sample mean for each pair. (Points: 6) Texas and Alaska * 13 - 01 = 5.5366 - 5.1466 / (V0.1004/6) = 0.39 /0.1293 = 3.0162 Texas and Florida * 13 - U2= 5.5366 - 4.92 / 0.1293 = 4.7687 Alaska and Florida . W1 - u2 = 5.1466 - 4.92 / 0.1293 = 1.7525 (iii) What is the critical value from the Studentized range distribution (from the Table reporting the critical values for Tukey's test)? (Points: 2) . Critical = 3.673 (iv) For each pair, state whether you reject or fail to reject the null hypothesis. (Points: 2) Texas and Alaska * us - 01 = Fail to reject Texas and Florida * 13 - U2 = Reject HO Alaska and Florida * 01 - u2 = Fail to reject 16(v) Summarize the conclusions of Tukey's test in a figure by underlying population means which are not significantly different from each other. (Points: 2) Texas and Alaska Texas and Florida * U3 - U2 Alaska and Florida . Uj - U2 (vi) What do you conclude about the mean acidity of rain among Alaska, Florida, and Texas? Elaborate. (Points: 2) 17