G Recall the method used to obtain a confidence interval for the difference between two population means for matched samples. (a) The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 − Population 2.) Element Population Difference 1 2 1 11 8 2 7 8 3 9 6 4 12 7 5 13 10 6 15 15 7 15 14

The difference value for each of the given element of both population is respectively; (5, 1, 5, 7, 5, 2, 3)

We are given the following data;

Population 1: 11, 7, 9, 12, 13, 15, 15

Population 2: 6, 6, 4, 5, 8, 13, 12

The difference value for each element is gotten from finding;

Population 1 - Population 2. Thus;

Difference value of element 1 = 11 - 6 = 5

Difference value of element 2 = 7 - 6 = 1

Difference value of element 3 = 9 - 4 = 5

Difference value of element 4 = 12 - 5 = 7

Difference value of element 5 = 13 - 8 = 5

Difference value of element 6 = 15 - 13 = 2

Difference value of element 7 = 15 - 12 = 3

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Step-by-step explanation:

Population 1: 11, 7, 9, 12, 13, 15, 15

Population 2: 6, 6, 4, 5, 8, 13, 12

Mean = sum of terms/number of terms

For population 1,

number of terms = 7

Mean = (11 + 7 + 9 + 12 + 13 + 15 + 15)/7 = 82/7 = 11.7

For population 2,

Number of terms = 7

Mean = (6 + 6 + 4 + 5 + 8 + 13 + 12)/7 = 7.71

The difference value for each element is

(11 + 7 + 9 + 12 + 13 + 15 + 15) - (6 + 6 + 4 + 5 + 8 + 13 + 12) = (5, 1, 5, 7, 5, 2, 3)

The difference between the two means is

Mean of population 1 - mean of population 2

Difference = 11.7 - 7.71 = 3.99