Question

Asked Oct 8, 2019

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In studying the relationship between age and time spent exercising, suppose you computed r=−0.307 using n=20 data points. Using the critical values table below, determine if the value of r is significant or not.

df |
CV (+ and -) |
df |
CV (+ and -) |
df |
CV (+ and -) |
df |
CV (+ and -) |
---|---|---|---|---|---|---|---|

1 | 0.997 | 11 | 0.555 | 21 | 0.413 | 40 | 0.304 |

2 | 0.950 | 12 | 0.532 | 22 | 0.404 | 50 | 0.273 |

3 | 0.878 | 13 | 0.514 | 23 | 0.396 | 60 | 0.250 |

4 | 0.811 | 14 | 0.497 | 24 | 0.388 | 70 | 0.232 |

5 | 0.754 | 15 | 0.482 | 25 | 0.381 | 80 | 0.217 |

6 | 0.707 | 16 | 0.468 | 26 | 0.374 | 90 | 0.205 |

7 | 0.666 | 17 | 0.456 | 27 | 0.367 | 100 | 0.195 |

8 | 0.632 | 18 | 0.444 | 28 | 0.361 | ||

9 | 0.602 | 19 | 0.433 | 29 | 0.355 | ||

10 | 0.576 | 20 | 0.423 | 30 | 0.349 |

Select the correct answer below:

1) r is significant because it is between the positive and negative critical values.

2) r is not significant because it is between the positive and negative critical values.

3) r is significant because it is not between the positive and negative critical values.

4) r is not significant because it is not between the positive and negative critical values.

Step 1

The degrees of freedom is n–2=20–2=18.

Step 2

*Rejection rule:*

If r is not lies between positive negative critical values, then the correlation is significant.

If r lies between positive negative critical values, then the correlation is not significant.

From the given critical value table, the critical value for degrees of freedom 18 is ±0.444.

Step 3

*Conclusion:*

Here, the value of r is –0.307, which lies between ±0.444.

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