length/cm |
---|

22 |

26 |

27 |

28 |

24 |

24 |

24 |

29 |

30 |

31 |

26 |

27 |

21 |

27 |

29 |

29 |

25 |

27 |

23 |

30 |

A study of the length in centimeters of
*Cephalopholis argus* [English: Peacock hind or blue-spotted grouper, Kosraen: Kalsrik, Mortlockese: Sawei, Mwoakillese: Widir, Pohnpeian: Mwoalusulus, Woleaian: Hali] found in the markets on Pohnpei from January to May 2006 was done by Kevin Rhodes, M. Tupper, Scotty Malakai, Don Jack, Clement Wichilmel, Richard Ben, and Kirino and Anson Olpet. The data is based loosely on this work. For the purposes of this quiz, consider that the average length for a population of blue-spotted groupers which has not been overharvested is μ = 30 centimeters. In other words, 30 cm is the mean for a healthy grouper population.

- __________ What is the level of measurement?
- __________ Find the sample size n.
- __________ Find the minimum.
- __________ Find the maximum.
- __________ Find the range.
- __________ Find the mode.
- __________ Find the median.
- __________ Find the sample mean x.
- __________ Find the midrange.
- __________ Find the sample standard deviation sx.
- __________ Find the sample coefficient of variation CV.
- __________ What is the point estimate for the population mean μ based on the sample mean x?

Consider a null hypothesis for which H_{0}: μ = 30

and an alternate hypothesis for which H_{1}: μ ≠ 30

Run a hypothesis test at a risk of a type I error α = 0.05

- ____________________ Calculate the value of t
_{critical} - ____________________ Calculate the value of t-statistic t
- _________________________________ Do we "reject" or "fail to reject" the null hypothesis?
- ____________________ Is the sample mean x statistically significantly different from the population mean for a an unharvested, healthy population?

Hypothesis Testing | |||
---|---|---|---|

Statistic or Parameter | Symbol | Equations | OpenOffice |

Relationship between confidence level c and alpha α for two-tailed tests | 1 − c = α | ||

Calculate t-critical for a two-tailed test | t_{c} | =TINV(α;df) | |

Calculate a t-statistic t | t | =(x - μ)/(sx/SQRT(n)) | |

Calculate a two-tailed p-value from a t-statistic | p-value | = TDIST(ABS(t);df;2) | |

Calculate a p-value for the difference of the means from two samples of paired samples | =TTEST(data_range_x;data_range_y;2;1) | ||

Calculate a p-value for the difference of the means from two independent samples, no presumption that σ_{x} = σ_{y} |
=TTEST(data_range_x;data_range_y;2;3) |