A Random Sample Of Five Observations From Three Normally Distributed Populations Produced The Following Data You May F 1 (39.69 KiB) Viewed 41 times
A random sample of five observations from three normally distributed populations produced the following data: (You may find it useful to reference the F table.) A 22 30 29 21 26 = 25.6 IB = 16.3 Grand mean Treatments B 24 30 16 28 25 Click here for the Excel Data File a. Calculate the grand mean. (Round Intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) SSTR MSTR R= 23.0 - 28.0 b. Calculate SSTR and MSTR. (Round Intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) SSE MSE C 26 23 18 22 16 20=21.0 st:- 16.0 c. Calculate SSE and MSE. (Round Intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) d. Specify the competing hypotheses in order to determine whether some differences exist between the population means. Test statistic ⒸHg: HA HB HC HA: Not all population means are equal. O Hg: HA ≤ HB ≤ HC HA: Not all population means are equal. ⒸHg: HA 2 HB 2 HC HA: Not all population means are equal. e-1. Calculate the value of the F(df1, df2₂) test statistic. (Round Intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
e-2. Find the p-value. O p-value ≥ 0.10 0.05 s p-value < 0.10 O 0.025 < p-value < 0.05 O 0.01 s p-value < 0.025 O p-value < 0.01 f. At the 1% significance level, what is the conclusion to the test? O Do not reject H₂ since the p-value is not less than significance level. O Reject H₂ since the p-value is less than significance level. O Reject H₂ since the p-value is not less than significance level. O Do not reject H since the p-value is less than significance level. g. Interpret the results at x = 0.01. O We conclude that some means differ. O We cannot conclude that some means differ. O We cannot conclude that all means differ. O We cannot conclude that population mean C is greater than population mean A.
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