# HW 8 - (e Consider the following If the process of...

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STATISTICS 321 – Homework 8 – due Tuesday, June 2, 2009 1. Suppose that a random sample of 50 bottles of a paricular brand of cough syrup is selected and the alcohol content of each bottle is determined. Let μ denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% conﬁdence interval is (7.8,9.4). (a) Would a 90% conﬁdence interval calculated from this same sample be wider or narrower than the given interval? Explain your reasoning. (b) Consider the following: We are 95% conﬁdent that the mean acohol content of the 50 bottles under study is between 7.8 and 9.4. Is this statement correct? Why or why not? (c) Consider the following: There is a 95% chance that μ is between 7.8 and 9.4. Is this statement correct? Why or why not? (d) Consider the following: We can be highly conﬁdent that 95% of all bottles of this type of cough syrup have an alcohol content that is between 7.8 and 9.4. Is this statement correct? Why or why not?
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Unformatted text preview: (e) Consider the following: If the process of selecting a sample of size 50 and then computing 95% condence intervals is repeated 100 times, 95 of the resulting intervals will include . Is this statement correct? Why or why not? 2. A condence interval is desired for the strayload loss (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray load loss is normally distributed with = 3 . 0. (a) Compute a 95% CI for when n = 25 and x = 58 . 3. (b) Compute a 95% CI for when n = 100 and x = 58 . 3. (c) How and why do your answers from (a) and (b) dier? (d) Compute a 99% CI for when n = 100 and x = 58 . 3. (e) Compute a 82% CI for when n = 100 and x = 58 . 3. (f) How and why do your answers from (b), (d) and (e) dier? (g) How large must n be if the width of the 99% interval for to be 1.0? 3. Section 5.3 : 5, 8, 14. 1...
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