1. Suppose you take independent random samples from populations with means and and standard...

   

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1. Suppose you take independent random samples from populations with means μ₁ and μ₂ and standard deviations ₁1 and 0₂. Furthermore, assume either that (i) both populations have normal distributions, or (ii) the sample sizes (n₁ and n₂) are large. If X₁ and X₂ are the random sample means, then (x₁-x₂)-(H1-H₂) how does the quantity behave? Give the + n1 nz name of the distribution and any parameters needed to describe it. 2. Suppose you take independent random samples from populations with means μ₁ and μ₂. Furthermore, assume either that (i) both populations have normal distributions, or (ii) the sample sizes (n₁ and n₂) are large. If X₁ and X₂ are the random sample means, and S₁ and S₂ are the random sample standard deviations, then how does the quantity (x₂-x₂)-(H₁-H₂) 122 behave? Give the name of the distribution and any parameters needed to describe it. 3. An ACME Bearings manager wants to compare the average ball bearing sizes from two different machines. She suspects the mean diameter for bearings from machine 2 exceeds that of bearings from machine 1. She takes two independent, random samples of size 50, one from each machine. The mean and standard deviation of bearings taken from machine 1 are 3.302 mm and 0.051 mm. The mean and standard deviation of bearings taken from machine 2 are 3.355 mm and 0.050 mm. Run a hypothesis test consistent with her suspicions. Be sure to a. check all necessary assumptions; b. state the null and alternative hypotheses; c. decide whether or not to pool and explain why; d. calculate the test statistic and p-value; e. state your conclusion in a complete sentence based on the p-value. 4. Use the data from the previous problem to make a 98% t-interval for the difference between the true means. In doing so, be sure to a. check all necessary assumptions for making the t-interval; b. calculate the interval endpoints; c. interpret the interval in a complete sentence. 1. Suppose you take independent random samples from populations with means μ₁ and μ₂ and standard deviations ₁1 and 0₂. Furthermore, assume either that (i) both populations have normal distributions, or (ii) the sample sizes (n₁ and n₂) are large. If X₁ and X₂ are the random sample means, then (x₁-x₂)-(H1-H₂) how does the quantity behave? Give the + n1 nz name of the distribution and any parameters needed to describe it. 2. Suppose you take independent random samples from populations with means μ₁ and μ₂. Furthermore, assume either that (i) both populations have normal distributions, or (ii) the sample sizes (n₁ and n₂) are large. If X₁ and X₂ are the random sample means, and S₁ and S₂ are the random sample standard deviations, then how does the quantity (x₂-x₂)-(H₁-H₂) 122 behave? Give the name of the distribution and any parameters needed to describe it. 3. An ACME Bearings manager wants to compare the average ball bearing sizes from two different machines. She suspects the mean diameter for bearings from machine 2 exceeds that of bearings from machine 1. She takes two independent, random samples of size 50, one from each machine. The mean and standard deviation of bearings taken from machine 1 are 3.302 mm and 0.051 mm. The mean and standard deviation of bearings taken from machine 2 are 3.355 mm and 0.050 mm. Run a hypothesis test consistent with her suspicions. Be sure to a. check all necessary assumptions; b. state the null and alternative hypotheses; c. decide whether or not to pool and explain why; d. calculate the test statistic and p-value; e. state your conclusion in a complete sentence based on the p-value. 4. Use the data from the previous problem to make a 98% t-interval for the difference between the true means. In doing so, be sure to a. check all necessary assumptions for making the t-interval; b. calculate the interval endpoints; c. interpret the interval in a complete sentence.

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