Question: Suppose a manufacturer has two assembly lines producing the same component, and they are measuring the length of the components for quality control. They know

Suppose a manufacturer has two assembly lines producing the same component, and they are measuring the length of the components for quality control. They know that the components produced by both assembly lines are normally distributed and that the population variances are equal. They take a sample of 50 units from each assembly line. Sample mean and standard deviation are shown below.

Line 1 Line 2

Sample Mean=20 Sample Mean=22

Sample SD=1.1 Sample SD=1.02

a. Construct a 90% confidence interval for the difference of the two means.

b. What is the null and alternative hypothesis?

c. Is the null hypothesis rejected at 10% significance (alpha = 0.1)?

d. Rework problem for a 95% confidence interval. Is the null hypothesis rejected? What, if anything, does this tell you about the p-value for this test?

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