Question

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?

*r*_{c.v.} =

What is the correlation coefficient for this data set?

*r* =

Your final conclusion is that...

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

Note: Round to three decimal places when necessary.

Please show how to solve with a TI-84 calculator. This is the only way I can solve. Thank you!

Answer #1

Level of significance = 0.01

Sample size = n = 17

Degrees of freedom = n - 2 = 17 - 2 = 15

**Critical value = c.v = 0.606**

Now we have to find the correlation coefficient (r)

By using TI-84 calculator we have to find correlation coefficient.

Click on STAT -------> Edit -------> Enter x values into L1 and y values into L2.

Then click 2ND -------> 0 ( Zero) ---------> DiagnosticOn ------->Enter

Then click on STAT ---------> CALC --------> LinReg( a + bx) -------->

Xlist: L1

Ylist: L2

FreqList:

Store RegEQ:

Calculate

We get

The correlation coefficient = r = 0.1463

Critical value > r we fail to reject null hypothesis.

Conclusion:

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

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=0.10. 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
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You wish to determine if there is a linear correlation between
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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
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Klr
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Dck
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FR
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