Question

The following data refers to yield of tomatoes (kg/plot) for four different levels of salinity. Salinity level here refers to electrical conductivity (EC), where the chosen levels were EC = 1.6, 3.8, 6.0, and 10.2 nmhos/cm. (Use i = 1, 2, 3, and 4 respectively.) 1.6: 59.7 53.5 56.2 63.7 58.8 3.8: 55.9 59.1 52.3 54.2 6.0: 51.3 48.8 53.6 48.5 10.2: 44.6 48.9 41.0 47.1 46.8 Use the F test at level a = 0.05 to test for any differences in true average yield due to the different salinity levels. State the appropriate hypotheses. Ho: H1 = 42 = 13 = 14 Ha: at least two hi's are unequal O Ho: 41 7 42 # 43 #444 Ha: at least two ui's are equal Ho: Mi = H2 = 13 = 114 Ha: all four 's are unequal Ho: M1 = 42 # 13 # 14 Ha: all four 's are equal Calculate the test statistic. (Round your answer to two decimal places.) f = 13.66 What can be said about the P-value for the test? OP-value > 0.100 O 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 P-value < 0.001

Answer 1

H: 14 = 4y = Uz = 44 Hat least two y's are unequal. EXCEL (Data Analysis) output:

Anova: Single Factor SUMMARY Groups Sample 1.6 Sample 3.8 Sample 6.0 Sample 10.2 Count 5 4 4 5 Sum 291.9 221.5 202.2 228.4 Average Variance 58.38 14.697 55.375 8.329167 50.55 5.71 45.68 9.177 of ANOVA Source of Variation Between Groups Within Groups Total SS 453.6509 137.6135 591.2644 MS F P -value F crit 3 151.217 15.38394 0.000104 3.343889 14 9.829536 17 The value of the test statistic is f = 15.38. P-value <0.001.