Hypothesis Testing- 2 samples

Ten individuals went on a low-fat diet for 12 weeks to lower their cholesterol. The data are recorded in the table below. Do you think that their cholesterol levels were significantly lowered? Conduct a hypothesis test at the 5% level.

Starting cholesterol level | Ending cholesterol level |
---|---|

140 | 140 |

220 | 240 |

110 | 130 |

240 | 220 |

200 | 190 |

180 | 150 |

190 | 200 |

360 | 300 |

280 | 300 |

260 | 240 |

NOTE: If you are using a Student’s *t*-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Part 1) State the distribution to use for the test. (Enter your answer in the form *z* or *t*_{df} where *df* is the degrees of freedom.)

Part 2) What is the test statistic? (If using the *z* distribution round your answer to two decimal places, and if using the *t* distribution round your answer to three decimal places.)

z or t= _______

Part 3) What is the *p*-value? (Round your answer to four decimal places.)

**Ten individuals went on a low-fat diet for 12 weeks to lower their cholesterol. The data are recorded in the table below. Do you think that their cholesterol levels were significantly lowered? Conduct a hypothesis test at the 5% level.**

Starting cholesterol level | Ending cholesterol level |
---|---|

170 | 170 |

220 | 230 |

110 | 130 |

240 | 220 |

200 | 190 |

180 | 150 |

190 | 200 |

360 | 300 |

280 | 300 |

260 | 240 |

**1). What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)**

Ten individuals went on a low-fat diet for 12 weeks to lower their cholesterol. The data are recorded in the table below. Do you think that their cholesterol levels were significantly lowered? Conduct a hypothesis test at the 5% level.

Starting cholesterol level | Ending cholesterol level |
---|---|

170 | 170 |

220 | 230 |

110 | 130 |

240 | 220 |

200 | 190 |

180 | 150 |

190 | 200 |

360 | 300 |

280 | 300 |

260 | 240 |

NOTE: If you are using a Student’s *t*-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

1). State the distribution to use for the test. (Enter your answer in the form *z* or *t*_{df} where *df* is the degrees of freedom.)

2). What is the test statistic? (If using the *z* distribution round your answer to two decimal places, and if using the *t* distribution round your answer to three decimal places.)

3). What is the *p*-value? (Round your answer to four decimal places.)

4). Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the *p*-value.

5). (i) Alpha (Enter an exact number as an integer, fraction, or decimal.)

? = ______

(ii) Decision:

(iii) Reason for decision:

(iv) Conclusion:

(v) Explain how you determined which distribution to use.

Starting cholesterol level | Ending cholesterol level |
---|---|

170 | 170 |

220 | 230 |

110 | 130 |

240 | 220 |

200 | 190 |

180 | 150 |

190 | 200 |

360 | 300 |

280 | 300 |

260 | 240 |

1) Please show me the steps on how you got the Test Statistic and the p-value for this problem on your calculator

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