Question

You wish to determine if there is a linear correlation between
the two variables at a significance level of α=0.05α=0.05. You have
the following bivariate data set.

x | y |
---|---|

43.3 | -108.4 |

21.9 | 114.3 |

1.5 | 113.2 |

62.4 | 143.4 |

-2.2 | 48.1 |

20.3 | -32.4 |

36.5 | 62.5 |

20.5 | 93.2 |

-10 | -71.7 |

31.9 | -323.3 |

30.9 | 132.5 |

51.2 | -276.3 |

29.5 | -3.4 |

2.9 | -28.1 |

7.4 | 277.4 |

31.7 | 194.3 |

25.2 | -120.5 |

12.6 | -113.8 |

33.5 | 494.4 |

28.8 | -99.9 |

37.1 | 229.6 |

11.7 | -196.9 |

39.1 | -295.9 |

18.7 | -192.7 |

-1.1 | -355.2 |

20.5 | 219.1 |

19.3 | -106.6 |

44.1 | 88.8 |

50.6 | 89 |

11.9 | -5.3 |

48.9 | 100.4 |

38.9 | -28.8 |

18.8 | 107.4 |

34.8 | 48.7 |

57.6 | 54.8 |

27.4 | 85.3 |

59.5 | 255.2 |

18.1 | -161.6 |

29.8 |
-221.4 |

What is the correlation coefficient for this data set?

*r* =

To find the p-value for a correlation coefficient, you need to
convert to a *t*-score:

t=√r2(n−2)1−r2t=r2(n-2)1-r2

This *t*-score is from a *t*-distribution with
*n*–2 degrees of freedom.

What is the p-value for this correlation coefficient?

p-value =

Answer #1

The statistical software output for this problem is :

**r = 0.1889**

**t = 1.1703**

**P-value = 0.2494**

You wish to determine if there is a linear correlation between
the two variables at a significance level of α=0.10. You have the
following bivariate data set.
x
y
41.4
82.8
48.4
97.1
49.9
89.8
47
92.8
20.5
63.7
40.5
74.3
33
70.2
25.9
64.9
29.1
66.1
28.7
80.2
9.7
41.8
23.2
50.3
13.4
49
-5.2
25.4
23.8
56.2
22.5
53.3
30.9
67.4
7
39.6
18.7
46.4
10.5
25.8
What is the correlation coefficient for this data set?
r =...

You wish to determine if there is a positive linear correlation
between the two variables at a significance level of α=0.01α=0.01.
You have the following bivariate data set.
x
y
54.5
82.1
45.8
20.9
46.4
22.7
44.8
-5.5
38.8
-5.4
35.4
83.5
44.3
96.3
25
-45.1
47.8
29.8
48.8
6
49.9
40.6
50.2
62.7
42.1
20.4
32.3
-40.2
45.1
30.5
49.3
3.4
29.4
27.7
44
2.3
39.2
18.2
37.5
1
44.1
27.1
50.6
-41.3
42.9
90.5
39.2
4.5
40.2
-60.7...

You wish to determine if there is a linear correlation between
the two variables at a significance level of α=0.01. You have the
following bivariate data set.
x
y
8.8
46.6
30.2
68.7
42.7
61.8
30.8
83.1
27.3
45.1
26.9
46.1
32
110.2
9.2
25.9
18.4
102.7
42
51.8
10.4
86.1
46.3
41.1
12.7
42.9
19.6
27.3
22.9
59.5
26.9
59.7
2.4
46.8
What is the critical value for this hypothesis test?
rc.v. =
What is the correlation coefficient for...

You wish to determine if there linear correlation between the
age of a driver and the number of driver deaths. The following
table represents the age of a driver and the number of driver
deaths per 100,000. Use a significance level of 0.05 and round all
values to 4 decimal places.
Driver Age
Number of Driver Deaths per 100,000
28
22
26
30
56
30
52
23
77
33
36
22
78
22
38
26
77
36
62
30
Ho:...

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