Question

Given two dependent random samples with the following results:

Population 1 | 20 | 22 | 44 | 42 | 28 | 48 | 39 |
---|---|---|---|---|---|---|---|

Population 2 | 30 | 30 | 32 | 45 | 18 | 43 | 32 |

Use this data to find the 99% confidence interval for the true difference between the population means. Assume that both populations are normally distributed.

Copy Data

Step 1 of 4 :

Find the point estimate for the population mean of the paired differences. Let x1 be the value from Population 1 and x2 be the value from Population 2 and use the formula d=x2−x1 to calculate the paired differences. Round your answer to one decimal place.

Step 2 of 4:

Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places.

Step 3 of 4:

Use the 99% confidence interval for the true difference between the population means. Assume that both populations are normally distributed.

Step 4 of 4:

Construct the 99% confidence interval. Round our answers to one decimal places.

Answer #1

Number | X2 | X1 | Difference | |

30 | 20 | 10 | 140.5918 | |

30 | 22 | 8 | 97.1633 | |

32 | 44 | -12 | 102.8776 | |

45 | 42 | 3 | 23.5918 | |

18 | 28 | -10 | 66.3061 | |

43 | 48 | -5 | 9.8776 | |

32 | 39 | -7 | 26.4490 | |

Total | 230 | 243 | -13 | 466.8571 |

Step 1

Point Estimate =

Step 2

Step 4

Confidence Interval :-

Critical value

Lower Limit =

Lower Limit = -14.2

Upper Limit =

Upper Limit = 10.5

**99% Confidence interval is ( -14.2 , 10.5 )**

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