Question

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* =

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

t=√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 =

Your final conclusion is that...

- There is sufficient sample evidence to support the claim that there is a statistically significant correlation between the two variables.
- There is insufficient sample evidence to support the claim the there is a correlation between the two variables.

Note: In your calculations, round both r and t to 3 decimal places
in ALL calculations.

Answer #1

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=0.05α=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...

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...

In each example, explain whether there is a significant linear
correlation between the two variables, and determine what
proportion of the variation can be explained by the linear
association between the variables: Linear correlation coefficient
between bear chest size and weight is 0.993, N = 21 Linear
correlation coefficient between the number of registered automatic
weapons and the murder rate is 0.885, N = 1000 Linear correlation
coefficient between the weight in female subjects and the BMI
metric is 0.936,...

Use the rank correlation coefficient to test for a
correlation between the two variables.
Ten trucks were ranked according to their comfort levels and their
prices.
Find the rank correlation coefficient and test the claim of
correlation between comfort and price. Use a significance level of
0.05.
rs= ?
critical values = ?

The covariance and correlation coefficient are measures that
quantify the non-linear relationship between two variables.
T/F

Correlation is a visual method for determining the relationship
between two variables... including linear, curve linear, strong,
weak, positive, negative, and no relationships. The correlation
coefficient is a mathematical reflection of that relationship.
Regression analysis is the same thing as the correlation
coefficient. True or False

Test the claim that the correlation between two variables is
zero when a sample of 19 points has the correlation coefficient of
0.46. Test with alpha = 0.01.

Suppose we have the correlation coefficient for the relationship
between two variables, A and B. Determine whether each of the
following statement is true or false.
(a) The variables A and B are categorical.
(b) The correlation coefficient tells us whether A or B is the
explanatory variable.
(c) If the correlation coefficient is positive, then lower values
of variable A tend to correspond to lower values of variable
B.
(d) If the correlation between A and B is r...

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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