Question

In: Statistics and Probability

The specification for the pull strength of a wire that connects an integrated circuit to its...

The specification for the pull strength of a wire that connects an integrated circuit to its frame is 10 g or more. In a sample of 88 units made with gold wire, 68 met the specification, and in a sample of 129 units made with aluminum wire, 105 met the specification. Let pX represent the population proportion units made with gold wire that meet the specification and let pY represent the population proportion units made with aluminum wire that meet the specification. Find a 95% confidence interval for the difference pX−pY . Round the answers to four decimal places.

The 95% confidence interval is ( , )

Expert Solution

Solution :

Given that,

₁ = x₁ / n₁ = 0.7727

₂ = x₂ / n₂ = 0.8140

1) Point estimate of difference between two proportions

= ₁ - ₂

= 0.7727 - 0.8140

= -0.0413

2)

Our aim is to construct 95% confidence interval.

= 1.96 (use z table)

Margin of error = *

=

= 0.1105

3) Required interval is

Point estimate Margin of error

-0.0413 0.1105

(-0.0413 - 0.1105, -0.0413 + 0.1105)

(-0.1518 , 0.0692)

orchestra answered 2 years ago

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