# B if instead of constructing a 95 confidence interval

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(b) If, instead of constructing a 95% confidence interval, the physician constructed a 90%confidence interval, would the 90% interval be wider, narrower, or the same width as the95% interval?Explain.(c) How would the width of confidence interval change if the physician took a largersample?Explain.
© 2011 BFW PublishersThe Practice of Statistics, 4/e- Chapter 8363Quiz 8.1CAP StatisticsName:1.Suppose you know that the distribution of finishing times for a certain crossword puzzle hasa mean of 25 minutes, a standard deviation of 8 minutes, and is moderately skewed left.Youtake an SRS of 45 finish times from this distribution and calculate the mean finish time,.(a) Describe the shape, center, and spread of the sampling distribution of.(b) Find a number,k, such that 95% of the values in the sampling distribution will lie withinkminutes of the mean of the distribution.(c) If you take repeated samples of size 45 from this population, what proportion of the timewill the intervalxkrcontain the number 25?Explain.xx
364The Practice of Statistics, 4/e- Chapter 8© 2011 BFW Publishers2.The confidence level is sometimes called the ―capture rate.‖Explain why this is anappropriate term.3.An insect ecologist reports a 95% confidence interval for the mean length of full-grownaquatic larvae of the Phantom MidgeChaoborus albatusto be 6.9 to 8.5 mm, based on asample of 9 individual larvae.(a) What are the point estimate and margin of error associated with this confidence interval?(b)The ecologist stated that ―all necessary conditions for constructing this confidenceinterval were met.‖What does this tell you about his methods and about the populationof insect larvae?(c) If the ecologist had reported a 99% confidence interval instead of a 95% interval, howwould it have been different?Explain.(d) The ecologist was unhappy with how wide this interval was.What should he do toproduce a narrower interval with the same level of confidence?Explain.
© 2011 BFW PublishersThe Practice of Statistics, 4/e- Chapter 8365Quiz 8.2AAP StatisticsName:1.A simple random sample of 1100 males aged 12 to 17 in the United States were askedwhether they played massive multiplayer online role-playing games (MMORPGs); 775 saidthat they did.We want to use this information to construct a 95% confidence interval toestimate the proportion of all U.S. males aged 12 to 17 who play MMORPGs.(a) State the parameter our confidence interval will estimate.(b) Identify each of the conditions that must be met to use this procedure, and explain howyou know that each one has been satisfied.(c) Find the appropriate critical value and the standard error of the sample proportion.(d) Give the 95% confidence interval.(e) Interpret the confidence interval constructed in part (d) in the context of the problem.
366The Practice of Statistics, 4/e- Chapter 8© 2011 BFW Publishers(f) Suppose you wanted to estimate the proportion of 12-to-17 year-old males who playMMORPG’s with 95% confidence to within ± 2%.Calculate how large a sample youwould need.

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