Question

In: Statistics and Probability

A random sample of five observations from three normally distributed populations produced the following data:

 

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.)

Treatments
A   B   C
  24       18       31  
  26       21       27  
  19       27       21  
  24       23       16  
  30       19       30  
x−Ax−A

=

24.6   x−Bx−B = 21.6   x−Cx−C = 25.0
s2AsA2 = 15.8   s2BsB2 = 12.8   s2CsC2 = 40.5
 

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.)

b. Calculate SSTR and MSTR. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

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.

  • H0: μA = μB = μC; HA: Not all population means are equal.

  • H0: μAμBμC; HA: Not all population means are equal.

  • H0: μAμBμC; HA: Not all population means are equal.

e-1. Calculate the value of the F(df1, df2) test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

e-2. Find the p-value.

  • p-value 0.10
  • 0.05 p-value < 0.10
  • 0.025 p-value < 0.05
  • 0.01 p-value < 0.025
  • p-value < 0.01

f. At the 1% significance level, what is the conclusion to the test?

  • Do not reject H0 since the p-value is not less than significance level.

  • Reject H0 since the p-value is less than significance level.

  • Reject H0 since the p-value is not less than significance level.

  • Do not reject H0 since the p-value is less than significance level.



g. Interpret the results at αα = 0.01.

  • We conclude that some means differ.

  • We cannot conclude that some means differ.

  • We cannot conclude that all means differ.

  • We cannot conclude that population mean C is greater than population mean A.

rev: 06_10_2019_QC_CS-170121

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