1 Consider a population with a known standard deviation of 15.4. In order to com
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Question
1
Consider a population with a known standard deviation of 15.4. In order to compute an interval estimate of the population mean, a sample of 35 observations is drawn. Use Table 1.
Compute the margin of error at a 90% confidence level. (Round your intermediate calculations to 4 decimal places. Round "z" value and final answer to 2 decimal places.)
Compute the margin of error at a 90% confidence level based on a larger sample of 310 observations.(Round your intermediate calculations to 4 decimal places. Round "z" value and final answer to 2 decimal places.)
Which of the two margins of error will lead to a wider confidence interval?
90% confidence with n = 310.
2
A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. They ask their realtor friend for help and she informs them that the last 29 houses that sold in their neighborhood took an average time of 230 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 35 days. Use Table 1.
What assumption regarding the population is necessary for making an interval estimate of the population mean?
Construct a 90% confidence interval of the mean sale time for all homes in the neighborhood.(Round your intermediate calculations to 4 decimal places, "z" value and final answers to 2 decimal places.)
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3
An article in the National Geographic News (“U.S. Racking Up Huge Sleep Debt,” February 24, 2005) argues that Americans are increasingly skimping on their sleep. A researcher in a small Midwestern town wants to estimate the mean weekday sleep time of its adult residents. He takes a random sample of 80 adult residents and records their weekday mean sleep time as 6.4 hours. Assume that the population standard deviation is fairly stable at 1.8 hours. Use Table 1.
Calculate a 95% confidence interval of the population mean weekday sleep time of all adult residents of this Midwestern town. (Round your intermediate calculations to 4 decimal places, "z" value and final answers to 2 decimal places.)
Can we conclude with 95% confidence that the mean sleep time of all adult residents in this Midwestern town is not 7 hours?
Consider a population with a known standard deviation of 15.4. In order to compute an interval estimate of the population mean, a sample of 35 observations is drawn. Use Table 1.
Explanation / Answer
1. A) b sample size is too small and population distribution is also unknown.
b) ME=zcritical*(sigma/sqrt N)=1.65(15.4/sqrt 35)=4.2951~4.30
c) ME=zcritical*(sigma/sqrt N)=1.65(15.4/sqrt 310)=1.4432~1.44
2. a) Population distribution has a normal distribution.
b) 90% c.i=Xbar+-zcritical (sigma/sqrt N)=230+-1.65(35/sqrt 29)=219.28 to 240.72
3. a) 95% c.i=6.4+-1.96(1.8/sqrt 80)=6 to 6.79
b) Yes, since the confidence interval does not contain 7.
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