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Batteries A company that produces AA batteries tests the
Chapter , Problem R8.3(choose chapter or problem)
Batteries A company that produces AA batteries tests the lifetime of a random sample of 40 batteries using a special device designed to imitate real-world use. Based on the testing, the company makes the following statement: Our AA batteries last an average of 430 to 470 minutes, and our confidence in that interval is 95%.\(^{''33}\)
(a) Determine the sample mean and standard deviation.
(b) A reporter translates the statistical announcement into plain English as follows: If you buy one of this companys AA batteries, there is a 95% chance that it will last between 430 and 470 minutes. Comment on this interpretation.
(c) Your friend, who has just started studying statistics, claims that if you select 40 more AA batteries at random from those manufactured by this company, there is a 95% probability that the mean life time will fall between 430 and 470 minutes. Do you agree? Explain.
(d) Give a statistically correct interpretation of the confidence interval that could be published in a newspaper report.
-Carry out the steps in constructing a confidence interval for a population proportion: define the parameter; check conditions; perform calculations; interpret results in context.
Questions & Answers
QUESTION:
Batteries A company that produces AA batteries tests the lifetime of a random sample of 40 batteries using a special device designed to imitate real-world use. Based on the testing, the company makes the following statement: Our AA batteries last an average of 430 to 470 minutes, and our confidence in that interval is 95%.\(^{''33}\)
(a) Determine the sample mean and standard deviation.
(b) A reporter translates the statistical announcement into plain English as follows: If you buy one of this companys AA batteries, there is a 95% chance that it will last between 430 and 470 minutes. Comment on this interpretation.
(c) Your friend, who has just started studying statistics, claims that if you select 40 more AA batteries at random from those manufactured by this company, there is a 95% probability that the mean life time will fall between 430 and 470 minutes. Do you agree? Explain.
(d) Give a statistically correct interpretation of the confidence interval that could be published in a newspaper report.
-Carry out the steps in constructing a confidence interval for a population proportion: define the parameter; check conditions; perform calculations; interpret results in context.
ANSWER:Step 1 of 4
(a) Sample mean and Standard deviation: Sample mean: Standard deviation: The 95% confidence interval is given by: Since the population is greater than 30, Margin of error is: Degree of freedom: Therefore the sample mean is 450 minutes and the standard deviation is 62.52 minutes.