Question

In studying the relationship between income and time spent exercising, suppose you computed r=−0.052 using n=19data 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:

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

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

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

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

Step 1

The provided value of correlation coefficient, r is -0.052 and the sample size, n is 19. So, the correlation coefficient is considered significant if the value of r is not lying in the range of critical value.

Step 2

The degrees of freedom, df = n-2, that is, 19-2 equals to 17. Therefore, the corresponding range of critical value from the provided table is (-0.456, +0.456). The provided value of r is lying between the ranges of cr...

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