**Practice Problems: t-test Answer **

A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. A pilot study was conducted to examine this hypothesis. Ten older adults (over the age of 70) and ten younger adults (between 20 and 30) were give a life satisfaction test (known to have high reliability and validity). Scores on the measure range from 0 to 60 with high scores indicative of high life satisfaction; low scores indicative of low life satisfaction. The data are presented below. Compute the appropriate t-test.

__Older Adults__ | __Younger Adults__ |

45 | 34 |

38 | 22 |

52 | 15 |

48 | 27 |

25 | 37 |

39 | 41 |

51 | 24 |

46 | 19 |

55 | 26 |

__46__ | __36__ |

Mean = 44.5 | Mean = 28.1 |

S = 8.682677518 | S = 8.543353492 |

S^{2} = 75.388888888 | S^{2} = 72.988888888 |

**Independent t-test**

- What is your computed answer? t
_{obs} = 4.257

- What would be the null hypothesis in this study? The null hypothesis would be that there are no significant differences between younger and older adults on life satisfaction.

- What would be the alternate hypothesis? The alternate hypothesis would be that life satisfaction scores of older and younger adults are different.

- What probability level did you choose and why? .05 - if one makes either a Type I or a Type II error, there will be no major risk involved.

- What is your t
_{crit}? t_{crit} = 2.101

- Is there a significant difference between the two groups? Yes, the t
_{obs} is in the tail. In fact, even if one uses a probability level the t is still in the tail. Thus, we conclude that we are 99.9 percent sure that there is a significant difference between the two groups.

- Interpret your answer. Older adults in this sample have significantly higher life satisfaction than younger adults (t = 4.257, p < .001). As this is a quasi-experiment, we can not make any statements concerning the cause of the difference.

- If you have made an error, would it be a Type I or a Type II error? Explain your answer. If an error was made, it would have to be a Type I error; there really are no differences in life satisfaction between younger and older adults. We just got these results by chance.

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