Question

Given two dependent random samples with the following results:

Population 1: 48, 18, 22, 31, 18, 26, 40

Population 2, 45, 28, 24, 19, 27, 36, 30

Use this data to find the 95% confidence interval for the true difference between the population means. Assume that both populations are normally distributed.

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: Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 4 of 4: Construct the 95% confidence interval. Round your answers to one decimal place.

Answer #1

Number | Population 2 | Population 1 | Difference | |

45 | 48 | -3 | 14.877551 | |

28 | 18 | 10 | 83.5918367 | |

24 | 22 | 2 | 1.30612245 | |

19 | 31 | -12 | 165.306122 | |

27 | 18 | 9 | 66.3061224 | |

36 | 26 | 10 | 83.5918367 | |

30 | 40 | -10 | 117.877551 | |

Total | 209 | 203 | 6 | 532.857143 |

Margin of Error =

Confidence Interval :-

Lower Limit =

Lower Limit = -7.8584

Upper Limit =

Upper Limit = 9.5727

95% Confidence interval is ( -7.9 , 9.6 )

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