Question

Suppose you are given the following x and y values. Assume x is the independent variable and y the dependent variable.

x | y |

13 | 10 |

10 | 11 |

3 | 4 |

29 | 23 |

5 | 8 |

25 | 21 |

8 | 10 |

17 | 15 |

19 | 17 |

31 | 29 |

23 | 24 |

Is there a significant relationship between x and y? Explain. Test at a 5% level of significance

Answer #1

X | Y | X * Y | |||

13 | 10 | 130 | 169 | 100 | |

10 | 11 | 110 | 100 | 121 | |

3 | 4 | 12 | 9 | 16 | |

29 | 23 | 667 | 841 | 529 | |

5 | 8 | 40 | 25 | 64 | |

25 | 21 | 525 | 625 | 441 | |

8 | 10 | 80 | 64 | 100 | |

17 | 15 | 255 | 289 | 225 | |

19 | 17 | 323 | 361 | 289 | |

31 | 29 | 899 | 961 | 841 | |

23 | 24 | 552 | 529 | 576 | |

Total | 183 | 172 | 3593 | 3973 | 3302 |

To Test :-

H0 :-

H1 :-

Test Statistic :-

t = 11.9701

Test Criteria :-

Reject null hypothesis if

Result :- Reject null hypothesis

Decision based on P value

P - value = P ( t > 11.97014052 ) = 0.00000079

Reject null hypothesis if P value <
level of significance

P - value = 0.00000079 < 0.05 ,hence we reject null
hypothesis

Conclusion :- We reject H0

There is statistically sufficient evidence to conclude that there is linear relationship between x and y.

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8
25
21
8
10
17
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19
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31
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____________________________________________
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