AP Statistics Practice Free Response Test – Chapter 10 ...



AP Statistics Practice Free Response Test – Chapter 10: Introduction to Inference

Instructions: Do all of the work for this practice test on your own paper.

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 σ = 0.02 cm. A large sample of 150 produced by the machine yields a sample mean diameter of 5.005 cm.

(a) Construct a 99% confidence interval for the true mean diameter of the rods produced by the milling machine.

(b) Does the interval in (a) give you reason to suspect that the machine is not producing rods of the correct diameter? Explain.

(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.

2. Statistics can help decide the authorship of literary works. Sonnets by an Elizabethan poet are known to contain an average of [pic] = 6.9 new words (words not used in the poet’s other works). The standard deviation of the number of new words is [pic] = 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 [pic] = 9.2 words not used in the poet’s known works. We expect poems by another author to contain more new words.

(a) State appropriate hypotheses in both words and symbols.

(b) Calculate the test statistic and the P-value.

(c) State your conclusion clearly in complete sentences.

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 [pic] = 50 dollars and that the mean for the original catalog will be [pic] = 25 dollars. You decide to use a sample size of n = 900.

(a) State appropriate hypotheses for a significance test, in sentence form.

(b) Explain what a Type I error is in this situation.

(c) Explain what a Type II error is in this situation.

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