Use the following to answer the questions below:

A Division III college men's basketball team is interested in identifying factors that impact the outcomes of their games. They plan to use "point spread" (their score minus their opponent's score) to quantify the outcome of each game this season; positive values indicate games that they won while negative values indicate games they lost. They want to determine if "steal differential" (the number of steals they have in the game minus the number of steals their opponent had) is related to point spread; positive values indicate games where they had more steals than their opponent. The data for the games they played this season displayed in the provided table.

Point Spread (y) | Steal Differential (x) | Point Spread (y) | Steal Differential (x) |

4 | 7 | 18 | -2 |

2 | -2 | 2 | 5 |

-21 | -2 | -6 | -6 |

-4 | 1 | 7 | 4 |

-9 | 2 | 13 | -1 |

7 | -5 | 3 | -3 |

-7 | 1 | 3 | 1 |

15 | -2 | 10 | -2 |

7 | -1 | 20 | 0 |

-13 | -2 | -1 | 1 |

-11 | -6 | -1 | -3 |

-17 | -3 | -11 | -2 |

31 | 7 | | |

Assuming that this season was a typical season for the team, they want to know if steal differential is positively correlated with point spread. Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that steal differential is positively correlated with point spread.

▸ Parameter:

ρ = correlation between point spread and steal differential for this team.

Hypotheses:

H_{0} :

ρ ≠ 0 versus

H_{a} :

ρ = 0

▸ Parameter:

ρ = correlation between point spread and steal differential for this team.

Hypotheses:

H_{0} :

ρ = 0 versus

H_{a} :

ρ < 0

▸ Parameter:

ρ = correlation between point spread and steal differential for this team.

Hypotheses:

H_{0} :

ρ = 0 versus

H_{a} :

ρ ≠ 0

▸ Parameter:

ρ = correlation between point spread and steal differential for this team.

Hypotheses:

H_{0} :

ρ = 0 versus

H_{a} :

ρ > 0