Question

Given two dependent random samples with the following results: Population 1 76 77 66 71 55 63 83 58 Population 2 78 71 71 65 61 71 77 62 Can it be concluded, from this data, that there is a significant difference between the two population means? Let d=(Population 1 entry)−(Population 2 entry). Use a significance level of α=0.1 for the test. Assume that both populations are normally distributed. Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Answer 1

Answer: Std = 6.0

Explanation:

Let us take a step by step process to solve this problem.

We have from the question that;

Population 1: 76 77 66 71 55 63 83 58

Population 2: 78 71 71 65 61 71 77 62

where n is no of occurrence = 8

taking the difference of P1 - P2 we have;

Difference (d) : -2 6 -5 6 -6 -8 6 -4

Total value of difference = -7

Difference squared (d₁ -d)² = 4 36 25 36 36 64 36 16

Total value of difference squared (d₁ -d)² = 253

The mean Σ = sum of values (d)/total value = -7/8 = -0.875

⇒ We are asked to find the value of the standard deviation of the paired difference.

Standard deviation is given as;

Std = √(Σ (Δd)² / n-1

Std = √[(253) / 8-1]

Std = √(253/7) = 6.0

Std = 6.0

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