<p> AP Statistics Practice Free Response Test – Chapter 10: Introduction to Inference</p><p>Instructions: Do all of the work for this practice test on your own paper.</p><p>1. A steel mill’s milling machine produces steel rods that are supposed to be 5 cm in diameter. When the machine is in statistical control, the rod diameters vary according to a normal distribution with mean µ = 5 cm and standard deviation  = 0.02 cm. A large sample of 150 produced by the machine yields a sample mean diameter of 5.005 cm.</p><p>(a) Construct a 99% confidence interval for the true mean diameter of the rods produced by the milling machine.</p><p>(b) Does the interval in (a) give you reason to suspect that the machine is not producing rods of the correct diameter? Explain.</p><p>(c) If the rod diameters did not already have a normal distribution, would it still be acceptable to construct the confidence interval in part (a)? Explain.</p><p>2. Statistics can help decide the authorship of literary works. Sonnets by an Elizabethan poet are known to contain an average of  = 6.9 new words (words not used in the poet’s other works). The standard deviation of the number of new words is  = 2.7. Now a manuscript with five new sonnets has come to light, and scholars are debating whether it is the poet’s work. The new sonnets contain an average of x = 9.2 words not used in the poet’s known works. We expect poems by another author to contain more new words.</p><p>(a) State appropriate hypotheses in both words and symbols.</p><p>(b) Calculate the test statistic and the P-value.</p><p>(c) State your conclusion clearly in complete sentences.</p><p>3. You want to see if a redesign of the cover of a mail-order catalog will increase sales. A very large number of customers will receive the original catalog and a random sample of customers will receive the one with the new cover. For planning purposes, you are willing to assume that the mean will be approximately normal with  = 50 dollars and that the mean for the original catalog will be  = 25 dollars. You decide to use a sample size of n = 900. </p><p>(a) State appropriate hypotheses for a significance test, in sentence form.</p><p>(b) Explain what a Type I error is in this situation.</p><p>(c) Explain what a Type II error is in this situation.</p><p></p>