Probability and Statistics for Engineering and the Sciences

9th Edition

ISBN: 9781305251809

Author: Jay L. Devore

Publisher: Cengage Learning

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Chapter 7.1, Problem 3E

Suppose that a random sample of 50 bottles of a particular 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 have been narrower or wider than the given interval? Explain your reasoning.
b. Consider the following statement: There is a 95% chance that μ is between 7.8 and 9.4. Is this statement correct? Why or why not?
c. Consider the following statement: 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?
d. Consider the following statement: If the process of selecting a sample of size 50 and then computing the corresponding 95% interval is repeated 100 times, 95 of the resulting intervals will include μ. Is this statement correct? Why or why not?

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Chapter 7 Solutions

Probability and Statistics for Engineering and the Sciences

Ch. 7.1 - Consider a normal population distribution with the...Ch. 7.1 - Each of the following is a confidence interval for...Ch. 7.1 - Suppose that a random sample of 50 bottles of a...Ch. 7.1 - A CI is desired for the true average stray-load...Ch. 7.1 - Assume that the helium porosity (in percentage) of...Ch. 7.1 - On the basis of extensive tests, the yield point...Ch. 7.1 - By how much must the sample size n be increased if...Ch. 7.1 - Let 1 0, 2 0, with 1 + 2 = . Then P(z1X-/nz2)=1-...Ch. 7.1 - a. Under the same conditions as those leading to...Ch. 7.1 - A random sample of n = 15 heat pumps of a certain...

Ch. 7.1 - Consider the next 1000 95% CIs for that a...Ch. 7.2 - The following observations are lifetimes (days)...Ch. 7.2 - The article Gas Cooking. Kitchen Ventilation, and...Ch. 7.2 - The negative effects of ambient air pollution on...Ch. 7.2 - Determine the confidence level for each of the...Ch. 7.2 - The alternating current (AC) breakdown voltage of...Ch. 7.2 - Exercise 1.13 gave a sample of ultimate tensile...Ch. 7.2 - The U.S. Army commissioned a study to assess how...Ch. 7.2 - The article Limited Yield Estimation for Visual...Ch. 7.2 - TV advertising agencies face increasing challenges...Ch. 7.2 - In a sample of 1000 randomly selected consumers...Ch. 7.2 - The technology underlying hip replacements has...Ch. 7.2 - The Pew Forum on Religion and Public Life reported...Ch. 7.2 - A sample of 56 research cotton samples resulted in...Ch. 7.2 - The Pew Forum on Religion and Public Life reported...Ch. 7.2 - The superintendent of a large school district,...Ch. 7.2 - Reconsider the CI (7.10) for p, and focus on a...Ch. 7.3 - Determine the values of the following quantities:...Ch. 7.3 - Determine the t critical value(s) that will...Ch. 7.3 - Determine the t critical value for a two-sided...Ch. 7.3 - Determine the t critical value for a lower or an...Ch. 7.3 - According to the article Fatigue Testing of...Ch. 7.3 - The article Measuring and Understanding the Aging...Ch. 7.3 - A sample of 14 joint specimens of a particular...Ch. 7.3 - Silicone implant augmentation rhinoplasty is used...Ch. 7.3 - A normal probability plot of the n = 26...Ch. 7.3 - A study of the ability of individuals to walk in a...Ch. 7.3 - Ultra high performance concrete (UHPC) is a...Ch. 7.3 - Exercise 72 of Chapter 1 gave the following...Ch. 7.3 - Prob. 40E Ch. 7.3 - A more extensive tabulation of t critical values...Ch. 7.4 - Determine the values of the following quantities:...Ch. 7.4 - Determine the following: a. The 95th percentile of...Ch. 7.4 - The amount of lateral expansion (mils) was...Ch. 7.4 - Wire electrical-discharge machining (WEDM) is a...Ch. 7.4 - Wire electrical-discharge machining (WEDM) is a...Ch. 7 - Example 1.11 introduced the accompanying...Ch. 7 - The article Distributions of Compressive Strength...Ch. 7 - For those of you who dont already know, dragon...Ch. 7 - A journal article reports that a sample of size 5...Ch. 7 - Unexplained respiratory symptoms reported by...Ch. 7 - High concentration of the toxic element arsenic is...Ch. 7 - Aphid infestation of fruit trees can be controlled...Ch. 7 - It is important that face masks used by...Ch. 7 - A manufacturer of college textbooks is interested...Ch. 7 - The accompanying data on crack initiation depth...Ch. 7 - In Example 6.8, we introduced the concept of a...Ch. 7 - Prob. 58SE Ch. 7 - Prob. 59SE Ch. 7 - Prob. 60SE Ch. 7 - Prob. 61SE Ch. 7 - Prob. 62SE

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