Two kinds of thread are being compared for strength. fifty pieces of each type of thread are tested under similar conditions. brand a has an average tensile strength of 78.3 kilograms with a standard deviation of 5.6 kilograms, while brand b has an average tensile strength of 87.2 kilograms with a standard deviation of 6.3 kilograms. construct a 95% confidence interval for the difference of the population means.

Question

Mathematics

Keenan Cobb

19 September, 11:43

Two kinds of thread are being compared for strength. fifty pieces of each type of thread are tested under similar conditions. brand a has an average tensile strength of 78.3 kilograms with a standard deviation of 5.6 kilograms, while brand b has an average tensile strength of 87.2 kilograms with a standard deviation of 6.3 kilograms. construct a 95% confidence interval for the difference of the population means.

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Luciano Travis · Answer 1

Let x = 78.3

y = 87.2

σₓ = 5.6 and σ₍y₎ = 6.3

number of pieces n = 50

z = z-score value = 1.96 in this case

A 100 (1-α) % confidence interval for the difference in large sample means is:

(x - y) ± z x √ (σₓ² / n + σ₍y₎² / n)

by putting the values,

= (78.3-87.2) ± 1.96 x √ (5.6² / 50 + 6.3² / 50)

= - 8.9 ± 2.34

= [-11.24, - 6.56]