Question

A group of adults with elevated cholesterol levels participated in a diet and exercise program to determine the effect of this program on their cholesterol. The resulting data follows:

Subject | Before | After |

1 | 259 | 244 |

2 | 260 | 250 |

3 | 272 | 246 |

4 | 260 | 235 |

5 | 281 | 273 |

6 | 254 | 245 |

Test the hypothesis that the diet and exercise program lowered the
subject's total chloresterol by **at least**

15 points. alpha = .05.

a. Find the mean of the
**differences**.

b. Find the standard deviation of the
**differences**.

c. Find the lower confidence limit of the
differences.

d. Find the upper confidence limit of the
differences.

e. According to the confidence interval, the null hypotesis that
the difference is equal to 20 cannot be rejected.

TRUE

FALSE

Please show work

Answer #1

Subject | Before | After | Difference |

1 | 259 | 244 | 15 |

2 | 260 | 250 | 10 |

3 | 272 | 246 | 26 |

4 | 260 | 235 | 25 |

5 | 281 | 273 | 8 |

6 | 254 | 245 | 9 |

Total | 93 |

Sample size = n = 6

a) Sample mean of difference = = 15.5

b) Standard deviation of difference = = 8.1179

c) We have to construct 95% confidence interval.

Formula is

Here E is a margin of error.

Degrees of freedom = n - 1 = 5 - 1 = 4

Level of significance = 0.05

tc = 2.571 ( Using t table)

So confidence interval is ( 15.5 - 8.5192 , 15.5 + 8.5192) =
> **( 6.9808 , 24.0192)**

c) Lower confidence limit = 6.9808

d) Upper confidence limit = 24.0192

e) TRUE because 20 is lies into interval.

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