Question 847934: 1. A tire manufacturer wishes to test a sample of its best=selling tire for average lifetime mileage. When the manufacturing process is operating properly, the standard deviation of the mileage is known to be 2,500. An SRS (simple random sample) of 100 tires is selected and is found to have a mean mileage of 59,500. You wish to construct a 95% confidence interval for the population mean.
A. Identify the population, the parameter about which we want to draw conclusions.
B. Verify that the necessary conditions exist for construction of a confidence interval.
C. Calculate a 95% confidence interval for population.
D. Interpret the confidence level of 95%.
E. What will happen to your confidence interval if your confidence level is raised to 99%?
Thank you so much for helping me in advance. I really don't understand this topic.. any help is appreciated! If you can, please guide me solve through the questions? Thank you!!!!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A tire manufacturer wishes to test a sample of its best=selling tire for average lifetime mileage. When the manufacturing process is operating properly, the standard deviation of the mileage is known to be 2,500. An SRS (simple random sample) of 100 tires is selected and is found to have a mean mileage of 59,500. You wish to construct a 95% confidence interval for the population mean.
A. Identify the population, the parameter about which we want to draw conclusions.
Pop:: All of the manufacturer's best-selling tire production.
Parameter: Population mean milage per tire.
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B. Verify that the necessary conditions exist for construction of a confidence interval.
Since every text is different, I'll leave that to you to look up in your text.
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C. Calculate a 95% confidence interval for population.
sample mean = x-bar = 59,500
ME = 1.96*2500/sqrt(100) = 490
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95% CI:: 59500-490 < u < 59500+490
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D. Interpret the confidence level of 95%.
We are 95% certain that the mean milage for that type tire is
between 59010 and 59990
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E. What will happen to your confidence interval if your confidence level is raised to 99%?
The z-value will be higher (2.5758), so ME will be larger, so the
confidence interval will be wider.
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cheers,
Stan H.
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