Chapter 14, Problem 11P

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8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

Identifying individuals with a high risk of Alzheimer’ disease usually involves a long series of cognitive tests. However, researchers have developed a 7-Minute Screen, which is a quick and easy way to accomplish the same goal. The question is whether the 7-Minute Screen is as effective as the complete series of tests. To address this question, Juin et al. (2008) administered both tests to a group of patients and compared the results. The following data represent results similar to those obtained in the study.

Patient |
7-Minute Screen |
Cognitive Series |

A | 3 | 11 |

B | 8 | 19 |

C | 10 | 22 |

D | 8 | 20 |

E | 4 | 14 |

F | 7 | 13 |

G | 4 | 9 |

H | 5 | 20 |

I | 14 | 25 |

**a.** Compute the Pearson correlation to measure the degree of relationship between the two test scores.

**b.** Is the correlation statistically significant? Use a two-tailed test with α = .01.

**c.** What percentage of variance for the cognitive scores is predicted from the 7-Minute Screen scores? (Compute the value of *r*^{2}.)

**a**.

To determine

The Pearson correlation of the given data.

Explanation

**Given info:**

The given data are shown below,

7-minut screen | Cognitive series |

3 | 11 |

8 | 19 |

10 | 22 |

8 | 20 |

4 | 14 |

7 | 13 |

4 | 9 |

5 | 20 |

14 | 25 |

**Calculation:**

Formula to calculate the Pearson correlation is,

Where co variability of the variable x and y is

Mean of the variable

Thus the mean of the variable

Mean of the variable

Thus the mean of the variable *Y* is 17.

For calculating

Sr |

**b**.

To determine

**To explain:** The correlation is statistically significant or insignificant using two tail test at 1% level of significance.

**c**.

To determine

The percentage of variance for the cognitive scores.

Sect-14.1 P-1LCSect-14.1 P-2LCSect-14.1 P-3LCSect-14.1 P-4LCSect-14.2 P-1LCSect-14.2 P-2LCSect-14.2 P-3LCSect-14.3 P-1LCSect-14.3 P-2LCSect-14.4 P-1LC

Sect-14.4 P-2LCSect-14.4 P-1LCASect-14.5 P-1LCSect-14.5 P-2LCSect-14.5 P-3LCSect-14.5 P-1LCASect-14.5 P-2LCASect-14.6 P-1LCSect-14.6 P-2LCSect-14.6 P-3LCSect-14.6 P-4LCSect-14.6 P-1LCASect-14.6 P-1LCBSect-14.6 P-2LCBSect-14.6 P-3LCBSect-14.6 P-1LCCCh-14 P-1PCh-14 P-2PCh-14 P-3PCh-14 P-4PCh-14 P-5PCh-14 P-6PCh-14 P-7PCh-14 P-8PCh-14 P-9PCh-14 P-10PCh-14 P-11PCh-14 P-12PCh-14 P-13PCh-14 P-17PCh-14 P-18PCh-14 P-19PCh-14 P-20PCh-14 P-21PCh-14 P-22PCh-14 P-23PCh-14 P-24PCh-14 P-25PCh-14 P-26PCh-14 P-27PCh-14 P-28PCh-14 P-29P

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