Question

A researcher records the following data for each of three groups.

Group A | Group B | Group C |
---|---|---|

3 | 5 | 11 |

7 | 9 | 1 |

9 | 3 | 11 |

9 | 9 | 7 |

12 | 14 | 10 |

What is the value of the *F*-statistic? (Round your answer
to two decimal places.)

*F* =

Explain your answer.

*F* is the indicated value because the group means are
the same. There is no variability between groups.*F* is the
indicated value because the group means are the same. There is
substantial variability between
groups. *F* is the indicated value
because the group means are different. There is no variability
between groups.*F* is the indicated value because the groups
means are different. There is substantial variability between
groups.

Answer #1

The test statistic can be written as

which under H_{0} follows a F distribution with df =
(df(Group), df(Error)) = (2,12)

We reject H_{0} at 5% level of significance if P-value
< 0.05

The value of the F statistic = 0

and P-value = 1

Since P-value = 1 > 0.05, so we fail to reject H_{0}
at 5% level of significance and we can conclude that the group
means are not significantly different.

ans-> **F is the indicated value because the group
means are the same. There is no variability between
groups.**

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