Question

Asked Jun 20, 2019

Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if there is a significant positive linear correlation between advertising cost and profit . Use a significance level of 0.05 and round all values to 4 decimal places.

Advertising Cost | Profit |
---|---|

3 | 23 |

4 | 20 |

5 | 27 |

6 | 25 |

7 | 30 |

8 | 23 |

9 | 21 |

10 | 23 |

11 | 33 |

12 | 29 |

Find p value.

Step 1

Let *r* denote the linear correlation between advertising cost (*x*) and profit (*y*). The hypotheses are given below:

*Null hypothesis:*

*H*_{0} : *r* = 0

That is, the sample correlation coefficient (*r*) is not significantly different from zero. There is no significant positive linear relationship between advertising cost and profit.

*Alternative hypothesis:*

*H*_{a} : *r* ≠ 0

That is, the sample correlation coefficient is significantly different from zero.

There is a significant positive linear relationship between advertising cost and profit.

Step 2

*Degrees of freedom:*

The formula for degrees of freedom is as follows:

Df = *n* – 2.

The number of data values given are 10, that is *n* = 10.

Substitute *n* = 10 in the degrees of freedom formula.

Df = *n* – 2 = 10 – 2 = 8.

The level of significance for the test is 0.05.

Step 3

*Sample correlation coefficient:*

The value of the sample correlation coefficient (*r*) can be obtained using Excel formula.

Enter the values of advertising cost in columns A2:A11 in Excel.

Enter the values...

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