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A random sample of 350 bolts from machine A contained 35 defective bolts, while an independently...

A random sample of 350 bolts from machine A contained 35 defective bolts, while an independently chosen, random sample of 250 bolts from machine B contained 17 defective bolts. Let P₁ be the proportion of the population of all bolts from machine A that are defective, and let P₂ be the proportion of the population of all bolts from machine B that are defective. Find a 99% confidence interval for P₁-P₂. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places. (If necessary, consult a list of formulas.) What is the lower limit of the 99% confidence interval? What is the upper limit of the 99% confidence interval?

Expert Solution

Let be the proportion of the population of all bolts from machine A that are defective, and let be the proportion of the population of all bolts from machine B that are defective

From the samples we know the following

Overall proportion of defects is

The standard error of the difference between 2 proportions is

We can use normal distribution as the approximation to the sampling distribution of difference in proportions.

The significance level for 99% confidence interval is

The right tail critical value is

Using the standard normal table we can get for z=2.58 P(Z<2.58) = 0.995.

Hence

99% confidence interval is

ans: The lower limit of the 99% confidence interval is -0.028

The upper limit of the 99% confidence interval is 0.092

milcah answered 1 year ago

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