Standard Error and Confidence Interval
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The Sony corporation produces a Walkman that requires two AA Batteries. The mean life of these batteries in this product is 35.0 hours. The distribtion of the battery lives closely follows the normal probability distribtion with a standard deviation of 5.5 hours. As a part of their testing program Sony tests samples of 25 batteries.
(a) What can you say about the shape of the distribution of sample mean?
(b) What is the standard error of the distribution of the sample mean?
(c) What proportion of the samples will have a mean useful life of more than 36 hours?
(d) What proportion of the sample will have a mean useful life greater than 34.5 hours?
(e) What proportion of the sample will have a mean useful life between 34.5 and 36.0 hours?
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The solution provides definitions and detail explanations of standard error and confidence interval. There are also links to several video presentations.
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(a) The shape of the distribution is bell-shaped, because it states that "The distribution of the battery lives closely follows the normal probability distribution" which is bell-shaped curve.
(b) If we take many random samples from a population and calculate their means and then take the standard deviation of those means, then we will call this standard deviation as standard error. In other words, the standard error tells us how accurate the sample mean is as compared to the population mean. The smaller the standard error the closer the sample mean to the population mean.
The formula for standard error is population standard deviation divided by the square root of the sample size. However, if the population variance is given then the ...
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