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Chapter 8: Q.31 (page 496)
98% Confidence find for aconfidence interval using table A or tour calculator. show your method.
The value of is
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Do you go to church? The Gallup Poll plans to ask a random sample of adults whether they attended a religious service in the last days. How large a sample would be required to obtain a margin of error of confidence interval for the population proportion who would say that they attended a religious service? Show your work.
- Construct and interpret a confidence interval for a population proportion.
- Explain how practical issues like nonresponse, under coverage, and response bias can affect the interpretation of a confidence interval.
Velvetleaf is a particularly annoying weed in cornfields. It produces lots of seeds, and the seeds wait in the soil for years until conditions are right for sprouting. How many seeds do velvetleaf plants produce? The Fathom histogram below shows the counts from plants that came up in a cornfield when no herbicide was used. Explain why it would not be wise to use a one-sample interval to estimate the mean number of seeds produced by velvetleaf plants.
To assess the accuracy of a laboratory scale, a standard weight known to weigh grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is grams if the scale has no bias). In previous studies, the standard deviation of the scale readings has been about gram. How many measurements must be averaged to get a margin of error of with confidence? Show your work.
R8.3. 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: 鈥淥ur AA batteries last an average of 430 to 470 minutes,
and our confidence in that interval is 95%.
(a) Determine the sample mean and standard deviation.
(b) A reporter translates the statistical announcement into 鈥減lain English鈥� as follows: 鈥淚f you buy one of this company鈥檚 AA batteries, there is a 95% chance that it will last between 430 and 470 minutes.鈥� 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.
Researchers were interested in comparing two methods for estimating tire wear. The first method used the amount of weight lost by a tire. The second method used the amount of wear in the grooves of the tire. A random sample of tires was obtained. Both methods were used to estimate the total distance traveled by each tire. The table below provides the two estimates (in thousands of miles) for each tire.
(a) Construct and interpret a confidence interval for the mean difference in the estimates from these two methods in the population of tires.
(b) Does your interval in part (a) give convincing evidence of a difference in the two methods of estimating tire wear? Justify your answer.
role="math" localid="1649913699288"
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